# LaTeX2HTML 2002 (1.62)
# Associate images original text with physical files.


$key = q/{displaymath}z_1=R(z)=z+frac{1}{2}R''(alpha)(z-alpha)^2+cdots{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="311" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img430.png"
 ALT="\begin{displaymath}
z_1 = R(z) = z + \frac{1}{2}R''(\alpha)(z-\alpha)^2 + \cdots
\end{displaymath}">|; 

$key = q/y>y_0>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1166.png"
 ALT="$y &gt; y_0 &gt; 0$">|; 

$key = q/{displaymath}R'(alpha)=+1,hspace{0.3in}R''(alpha)=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1257.png"
 ALT="\begin{displaymath}
R'(\alpha) = +1, \hspace{0.3in} R''(\alpha) = 0.
\end{displaymath}">|; 

$key = q/{displaymath}R'(z)=frac{2-(m-1)z^m}{(z^m+2)^2},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img1292.png"
 ALT="\begin{displaymath}
R'(z) = \frac{2 - (m - 1)z^m}{(z^m + 2)^2},
\end{displaymath}">|; 

$key = q/(C_{-(n-1)},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1456.png"
 ALT="$(C_{-(n-1)},$">|; 

$key = q/w_n^{p+2},dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img745.png"
 ALT="$w_n^{p+2}, \dots$">|; 

$key = q/displaystylefrac{m}{(m-1)^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1326.png"
 ALT="$\displaystyle\frac{m}{(m-1)^2}$">|; 

$key = q/displaystyle4sum^{frac{d^2-d}{2}}_{1}left(-frac{1}{2}-Pright)+sum^{d}_{1}left(-frac{1}{2}-Qright)+Releft(frac{1}{-s'-1}right)+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="441" HEIGHT="91" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$\displaystyle 4\sum^{\frac{d^2-d}{2}}_{1}\left(-\frac{1}{2} -P\right) + \sum^{d}_{1}\left(-\frac{1}{2} - Q\right) + \Re\left(\frac{1}{-s' - 1}\right) + 1$">|; 

$key = q/1^0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img683.png"
 ALT="$1^0$">|; 

$key = q/R(z)geq4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1273.png"
 ALT="$R(z) \geq 4$">|; 

$key = q/{displaymath}t=R'(z)R'(z_1)dotsR'(r_{n-1})=prod_{i=0}^{n=1}dz_i^{d-1}=d^n(Piz_i)^{d-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="434" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img914.png"
 ALT="\begin{displaymath}
t = R'(z)R'(z_1) \dots R'(r_{n-1}) = \prod_{i=0}^{n=1}dz_i^{d-1} = d^n(\Pi z_i)^{d-1}.
\end{displaymath}">|; 

$key = q/midR(z)mid>r';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1372.png"
 ALT="$\mid R(z)\mid &gt; r'$">|; 

$key = q/displaystylefrac{1}{d^n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1422.png"
 ALT="$\displaystyle\frac{1}{d^n}$">|; 

$key = q/R(alpha)=+1,;R''(alpha)neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1256.png"
 ALT="$R(\alpha) = +1,\; R''(\alpha) \neq 0$">|; 

$key = q/f(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img753.png"
 ALT="$f(z)$">|; 

$key = q/(mu,-infty);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1214.png"
 ALT="$(\mu, -\infty)$">|; 

$key = q/{displaymath}R(z)=alpha+(z-alpha)+frac{1}{l}(z-alpha)^2+cdotshspace{0.3in}left(R''(alpha)=frac{2}{l}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="462" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1025.png"
 ALT="\begin{displaymath}
R(z) = \alpha + (z - \alpha) + \frac{1}{l}(z - \alpha)^2 + \cdots \hspace{0.3in} \left(R''(\alpha) = \frac{2}{l} \right).
\end{displaymath}">|; 

$key = q/displaystylefrac{pi}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img637.png"
 ALT="$\displaystyle\frac{\pi}{2}$">|; 

$key = q/w=sqrt{z},;w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1462.png"
 ALT="$w = \sqrt{z},\; w$">|; 

$key = q/{displaymath}nsum^{frac{d^n-d}{n}}_{1}Releft(frac{1}{t-1}right)+sum^{d+1}_{1}Releft(frac{1}{s^n-1}right)+1=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="351" HEIGHT="67" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="\begin{displaymath}
n\sum^{\frac{d^n - d}{n}}_{1}\Re\left(\frac{1}{t-1}\right) + \sum^{d + 1}_{1}\Re\left(\frac{1}{s^n - 1}\right) + 1 = 0.
\end{displaymath}">|; 

$key = q/t_n=s^{pmn}t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img364.png"
 ALT="$t_n = s^{\pm n}t$">|; 

$key = q/n-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img274.png"
 ALT="$n-1$">|; 

$key = q/displaystylefrac{N+1}{midzmid};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img581.png"
 ALT="$\displaystyle\frac{N + 1}{\mid z\mid }$">|; 

$key = q/{displaymath}alpha=R_{p+k-h}(alpha)=R_q(alpha).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="\begin{displaymath}
\alpha = R_{p+k-h}(\alpha) = R_q(\alpha).
\end{displaymath}">|; 

$key = q/{displaymath}R_n(z)=s^nz+cdots{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img786.png"
 ALT="\begin{displaymath}
R_n(z) = s^nz + \cdots
\end{displaymath}">|; 

$key = q/{calL}N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img551.png"
 ALT="${\cal L}N$">|; 

$key = q/mid{z-alpha}midleqrho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img352.png"
 ALT="$\mid {z-\alpha}\mid \leq\rho$">|; 

$key = q/D^{(i)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img723.png"
 ALT="$D^{(i)}$">|; 

$key = q/{displaymath}z_n=z+na+thetasum_1^nfrac{C'Bgamma}{ngamma}hspace{0.3in}(midthetamid<1){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="320" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img486.png"
 ALT="\begin{displaymath}
z_n = z + na + \theta\sum_1^n\frac{C'B\gamma}{n\gamma} \hspace{0.3in}(\mid \theta\mid &lt; 1)
\end{displaymath}">|; 

$key = q/sigma_{-nh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1122.png"
 ALT="$\sigma_{-nh}$">|; 

$key = q/[z,R(z)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img996.png"
 ALT="$[z, R(z)]$">|; 

$key = q/midtmid>M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1359.png"
 ALT="$\mid t\mid &gt; M$">|; 

$key = q/(gamma-1)+(gamma'-1)+(gamma''-1)+cdots-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="301" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img333.png"
 ALT="$(\gamma - 1)+(\gamma' - 1)+(\gamma'' - 1)+ \cdots -$">|; 

$key = q/{displaymath}rho=e^{textstylec(omega+frac{2Npi}{q-1})},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img407.png"
 ALT="\begin{displaymath}
\rho = e^{\textstyle c(\omega + \frac{2N\pi}{q-1})},
\end{displaymath}">|; 

$key = q/{displaymath}F(z)=F(z_1)-a=z_1+o({calL}midz_1mid),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img593.png"
 ALT="\begin{displaymath}
F(z) = F(z_1) - a = z_1 + o({\cal L}\mid z_1\mid ),
\end{displaymath}">|; 

$key = q/midR(z)mid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1297.png"
 ALT="$\mid R(z) \mid $">|; 

$key = q/{displaymath}z_{-1}=z+az^2+cdots,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img634.png"
 ALT="\begin{displaymath}
z_{-1} = z + az^2 + \cdots ,
\end{displaymath}">|; 

$key = q/alpha,f(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img956.png"
 ALT="$\alpha, f(z)$">|; 

$key = q/r>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$r&gt;1$">|; 

$key = q/a_{-n}b_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1453.png"
 ALT="$a_{-n} b_{-n}$">|; 

$key = q/displaystyle-1+4sum^{frac{d^2-d}{2}}_{1}frac{1}{2}+sum^{d}_{1}frac{1}{2}+H,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="91" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$\displaystyle -1 + 4\sum^{\frac{d^2 - d}{2}}_{1}\frac{1}{2} + \sum^{d}_{1}\frac{1}{2} + H,$">|; 

$key = q/R'(z)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1373.png"
 ALT="$R'(z) = 0$">|; 

$key = q/frac{1}{z^h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img565.png"
 ALT="$\frac{1}{z^h}$">|; 

$key = q/{displaymath}t_n=p,a,n+frac{b}{pa}{calL}n+F(t)+varepsilon_n,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img714.png"
 ALT="\begin{displaymath}
t_n = p a n + \frac{b}{pa}{\cal L}n + F(t) + \varepsilon_n,
\end{displaymath}">|; 

$key = q/z_{lambda+mu},;z_{lambda'+mu'},;z_{lambda''+mu''},;dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img877.png"
 ALT="$z_{\lambda + \mu},\; z_{\lambda' + \mu'},\; z_{\lambda'' + \mu''},\; \dots$">|; 

$key = q/qgeq2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img925.png"
 ALT="$q \geq 2$">|; 

$key = q/{displaymath}a_{-p}=a_{-p-q}hspace{0.5in}(qgeq1),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="\begin{displaymath}
a_{-p} = a_{-p-q} \hspace{0.5in} (q\geq1),
\end{displaymath}">|; 

$key = q/Q(t)=L(2-e^t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img829.png"
 ALT="$Q(t)=L(2-e^t)$">|; 

$key = q/n^{0}11;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img722.png"
 ALT="$n^{0} 11$">|; 

$key = q/{displaymath}mid{log(1+w)}mid<midwmid+midwmid^2+midwmid^3+cdots<2midwmid,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="420" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img386.png"
 ALT="\begin{displaymath}
\mid {\log (1 + w)}\mid &lt; \mid w\mid + \mid w\mid ^2 + \mid w\mid ^3 + \cdots &lt; 2\mid w\mid ,
\end{displaymath}">|; 

$key = q/{C'}_{-(n+1)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1209.png"
 ALT="${C'}_{-(n+1)}$">|; 

$key = q/W=R_1(w);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1506.png"
 ALT="$W = R_1(w)$">|; 

$key = q/{displaymath}u+1<0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="\begin{displaymath}
u+1 &lt; 0,
\end{displaymath}">|; 

$key = q/delta,delta_1,dots,delta_{p-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img418.png"
 ALT="$\delta, \delta_1, \dots, \delta_{p-1}$">|; 

$key = q/{displaymath}array{{l}(sz+a_2z^2+cdots+a_hz^h+cdots)+A_h[sz+a_2z^2+cdots+a_hz^h+z+a_hz^h+cdots]^2+a_h[z+cdots]^h+Kz^{h+1},array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="542" HEIGHT="99" BORDER="0"
 SRC="|."$dir".q|img793.png"
 ALT="\begin{displaymath}
\begin{array}{l}
(sz + a_2z^2 + \cdots + a_hz^h + \cdots)
+...
...z^h + \cdots]^2 + a_h[z + \cdots]^h \\\\
+ Kz^{h+1},
\end{array}\end{displaymath}">|; 

$key = q/z_{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img299.png"
 ALT="$z_{-1}$">|; 

$key = q/midz_n-alphamid>k^nmidz-alphamid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img850.png"
 ALT="$\mid z_n - \alpha\mid &gt; k^n\mid z - \alpha\mid $">|; 

$key = q/left(displaystylefrac{pi}{p},frac{3pi}{p}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img668.png"
 ALT="$\left( \displaystyle\frac{\pi}{p}, \frac{3\pi}{p} \right)$">|; 

$key = q/R(z)=z^d+a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img908.png"
 ALT="$R(z) = z^d + a$">|; 

$key = q/{C'}_{-1},{C'}_{-2},dots,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1385.png"
 ALT="${C'}_{-1}, {C'}_{-2}, \dots,$">|; 

$key = q/(alpha_1alpha_2dotsalpha_ndots);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1417.png"
 ALT="$(\alpha_1 \alpha_2 \dots \alpha_n \dots)$">|; 

$key = q/s';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$s'$">|; 

$key = q/midz_{lambda'}-alphamid<rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img875.png"
 ALT="$\mid z_{\lambda'} - \alpha\mid &lt; \rho$">|; 

$key = q/sumdisplaystylefrac{2A}{q_n}mid{z_n}mid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img388.png"
 ALT="$\sum\displaystyle\frac{2A}{q_n}\mid {z_n}\mid $">|; 

$key = q/a_{-1}b''_{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1436.png"
 ALT="$a_{-1} b''_{-1}$">|; 

$key = q/displaystylefrac{d^2rho}{domega^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img462.png"
 ALT="$\displaystyle\frac{d^2\rho}{d\omega^2}$">|; 

$key = q/w_1=t_1^{-frac{1}{p}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img709.png"
 ALT="$w_1 = t_1^{-\frac{1}{p}}$">|; 

$key = q/displaystyleY=y+sumfrac{A}{(x-a)^2+y^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1235.png"
 ALT="$\displaystyle Y = y + \sum\frac{A}{(x - a)^2 + y^2}$">|; 

$key = q/{displaymath}R(z)=kz+h-sumfrac{A}{z-a},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img926.png"
 ALT="\begin{displaymath}
R(z) = kz + h - \sum\frac{A}{z-a},
\end{displaymath}">|; 

$key = q/s>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img985.png"
 ALT="$s &gt; 1$">|; 

$key = q/{displaymath}xi=frac{u-1}{u^2+v^2-2u+1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="\begin{displaymath}
\xi = \frac{u-1}{u^2 + v^2 - 2u + 1}.
\end{displaymath}">|; 

$key = q/q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$q$">|; 

$key = q/P;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$P$">|; 

$key = q/o({calL}midzmid);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img519.png"
 ALT="$o({\cal L}\mid z\mid )$">|; 

$key = q/B;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img227.png"
 ALT="$B$">|; 

$key = q/w_n^{v+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img744.png"
 ALT="$w_n^{v+1}$">|; 

$key = q/rho>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img351.png"
 ALT="$\rho &gt; 0$">|; 

$key = q/a_{-2}a_{-1}b_{-1}b_{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1443.png"
 ALT="$a_{-2}a_{-1}b_{-1}b_{-2}$">|; 

$key = q/(0<tleq1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1345.png"
 ALT="$(0 &lt; t \leq 1)$">|; 

$key = q/q>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="$q &gt; 1$">|; 

$key = q/{displaymath}frac{1}{s-1}=-1-{sum}'frac{1}{s-1}=-1-Phspace{0.1in}(P>0),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img981.png"
 ALT="\begin{displaymath}
\frac{1}{s-1} = -1 - {\sum}'\frac{1}{s-1} = -1-P \hspace{0.1in}(P&gt;0),
\end{displaymath}">|; 

$key = q/t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$t$">|; 

$key = q/displaystyle2+K,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$\displaystyle 2 + K,$">|; 

$key = q/{displaymath}R[G(Z)]=G(sZ).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img862.png"
 ALT="\begin{displaymath}
R[G(Z)] = G(sZ).
\end{displaymath}">|; 

$key = q/frac{1}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img711.png"
 ALT="$\frac{1}{t}$">|; 

$key = q/displaystylefrac{P(n)}{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1133.png"
 ALT="$\displaystyle\frac{P(n)}{n}$">|; 

$key = q/{displaymath}a=a_{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="\begin{displaymath}
a = a_{-1}.
\end{displaymath}">|; 

$key = q/C;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img245.png"
 ALT="$C$">|; 

$key = q/{displaymath}M^2(r)>r^2+n^2midamid^2r^{2(p+1)}+midbmid^2r^{2(p+2)}+cdots.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="399" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img780.png"
 ALT="\begin{displaymath}
M^2(r) &gt; r^2 + n^2\mid a \mid^2r^{2(p+1)} + \mid b \mid^2r^{2(p+2)} + \cdots.
\end{displaymath}">|; 

$key = q/{displaymath}0<k<1,hspace{0.3in}k+sumfrac{2A}{a^2}>1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1501.png"
 ALT="\begin{displaymath}
0 &lt; k &lt; 1, \hspace{0.3in} k + \sum\frac{2A}{a^2} &gt; 1.
\end{displaymath}">|; 

$key = q/(t)<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img919.png"
 ALT="$(t) &lt; 1$">|; 

$key = q/D,D_1,...,D_{p-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img337.png"
 ALT="$D, D_1, ..., D_{p-1}$">|; 

$key = q/{displaymath}z_n=z+na+H_nsum_1^nfrac{1}{ngamma},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img487.png"
 ALT="\begin{displaymath}
z_n = z + na + H_n\sum_1^n\frac{1}{n\gamma},
\end{displaymath}">|; 

$key = q/{Large{frac{1}{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img585.png"
 ALT="$\Large\frac{1}{N}$">|; 

$key = q/z=f(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1346.png"
 ALT="$z = f(t)$">|; 

$key = q/gamma^{n'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img305.png"
 ALT="$\gamma^{n'}$">|; 

$key = q/{calL}midzmid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img520.png"
 ALT="${\cal L}\mid z\mid $">|; 

$key = q/{displaymath}R_{q-1}(z)=overline{omega}+frac{1}{P(z)}=overline{omega}'+frac{1}{P'(z)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="282" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img222.png"
 ALT="\begin{displaymath}
R_{q-1}(z) = \overline{\omega} + \frac{1}{P(z)} = \overline{\omega}' + \frac{1}{P'(z)}.
\end{displaymath}">|; 

$key = q/alpha,alpha';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img998.png"
 ALT="$\alpha, \alpha'$">|; 

$key = q/A=A';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1489.png"
 ALT="$A=A'$">|; 

$key = q/Fleft[frac{1}{P^p(z)}right]=f(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img755.png"
 ALT="$F\left[ \frac{1}{P^p(z)} \right] = f(z) $">|; 

$key = q/b_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1401.png"
 ALT="$b_{-n}$">|; 

$key = q/z+2a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img444.png"
 ALT="$z + 2a$">|; 

$key = q/D_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img906.png"
 ALT="$D_3$">|; 

$key = q/t=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img365.png"
 ALT="$t = 0$">|; 

$key = q/alpha,alpha_1,...,alpha_{p-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$\alpha, \alpha_1, ..., \alpha_{p-1}$">|; 

$key = q/{displaymath}array{{rcccl}w&=&P(z)&=&z+lambda_2z^2+cdots+lambda_pz^p,w_1&=&P(z_1).&&array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="340" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img686.png"
 ALT="\begin{displaymath}
\begin{array}{rcccl}
w &amp; = &amp; P(z) &amp; = &amp; z + \lambda_2z^2 + \cdots + \lambda_pz^p, \\\\
w_1 &amp; = &amp; P(z_1). &amp; &amp;
\end{array}\end{displaymath}">|; 

$key = q/tneq+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$t\neq+1$">|; 

$key = q/{displaymath}midR'(z)mid>K>1{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1409.png"
 ALT="\begin{displaymath}
\mid R'(z)\mid &gt; K &gt; 1
\end{displaymath}">|; 

$key = q/midz_lambda-alphamid<rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img868.png"
 ALT="$\mid z_\lambda - \alpha\mid &lt; \rho$">|; 

$key = q/{displaymath}z_n=z+na+sum_0^{n-1}frac{b}{z_i}+sum_0^{n-1}chi(z_i),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="262" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img522.png"
 ALT="\begin{displaymath}
z_n = z + na + \sum_0^{n-1}\frac{b}{z_i} + \sum_0^{n-1}\chi(z_i),
\end{displaymath}">|; 

$key = q/z_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1239.png"
 ALT="$z_p$">|; 

$key = q/z=5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1268.png"
 ALT="$z = 5$">|; 

$key = q/vgeq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1097.png"
 ALT="$v \geq 1$">|; 

$key = q/s;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$s$">|; 

$key = q/framebox[0.75in]{{+inftyhspace{0.1in}+infty{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img950.png"
 ALT="\framebox[0.75in]{$+\infty \hspace{0.1in} +\infty$}">|; 

$key = q/e^{ibeta}z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img841.png"
 ALT="$e^{i\beta}z$">|; 

$key = q/te^{textstylefrac{2iphiN}{q^n}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="33" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img400.png"
 ALT="$te^{\textstyle\frac{2i\phi N}{q^n}}$">|; 

$key = q/{displaymath}midR'(z)mid>K>1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1414.png"
 ALT="\begin{displaymath}
\mid R'(z)\mid &gt; K &gt; 1,
\end{displaymath}">|; 

$key = q/midz_{lambda+mu}-alphamid<krho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img872.png"
 ALT="$\mid z_{\lambda + \mu} - \alpha\mid &lt; k\rho$">|; 

$key = q/{displaymath}d^{nd-d}Pi(z)^{d-1},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img915.png"
 ALT="\begin{displaymath}
d^{nd - d}\Pi (z)^{d-1},
\end{displaymath}">|; 

$key = q/z_1=sz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img825.png"
 ALT="$z_1 = sz$">|; 

$key = q/n(modp);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img340.png"
 ALT="$n (mod p)$">|; 

$key = q/y<-y_0<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1241.png"
 ALT="$y &lt; -y_0 &lt; 0$">|; 

$key = q/displaystyleR'(alpha_{p-1})F_p(z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img427.png"
 ALT="$\displaystyle R'(\alpha_{p-1})F_p(z),$">|; 

$key = q/-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$-1$">|; 

$key = q/D_{(i)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img749.png"
 ALT="$D_{(i)}$">|; 

$key = q/-R(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img989.png"
 ALT="$-R(z)$">|; 

$key = q/n>2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img995.png"
 ALT="$n &gt; 2$">|; 

$key = q/{cal{D}}_1=R({cal{D}});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1176.png"
 ALT="${\cal{D}}_1 = R({\cal{D}})$">|; 

$key = q/R(sigma)=-{Large{frac{1}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$R(\sigma) = -\Large\frac{1}{2}$">|; 

$key = q/+mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img474.png"
 ALT="$+\mu$">|; 

$key = q/{displaymath}R(z)+lambda=z{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="\begin{displaymath}R(z)+ \lambda = z
\end{displaymath}">|; 

$key = q/displaystylefrac{+1pmsqrt{6}}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img892.png"
 ALT="$\displaystyle\frac{+1 \pm \sqrt{6}}{2}$">|; 

$key = q/{displaymath}nsum^{frac{d^n-1}{n}}_{1}frac{1}{t-1}+sum^{d+1}_{1}beta_{n}(s)+1-frac{1}{n}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="67" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="\begin{displaymath}
n\sum^{\frac{d^n - 1}{n}}_{1}\frac{1}{t-1} + \sum^{d + 1}_{1}\beta_{n}(s) + 1 - \frac{1}{n} = 0,
\end{displaymath}">|; 

$key = q/{displaymath}f(z)=R(z)-z=h-z-sumfrac{A}{z-a}=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="330" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img946.png"
 ALT="\begin{displaymath}
f(z) = R(z) - z = h - z - \sum\frac{A}{z-a} = 0
\end{displaymath}">|; 

$key = q/{displaymath}midR'(z)mid>k>2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1276.png"
 ALT="\begin{displaymath}
\mid R'(z)\mid &gt; k &gt; 2.
\end{displaymath}">|; 

$key = q/z^h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img795.png"
 ALT="$z^h$">|; 

$key = q/omega=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img661.png"
 ALT="$\omega = 1$">|; 

$key = q/{displaymath}pmd^{dn-d}[P(a)]^{d-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img918.png"
 ALT="\begin{displaymath}
\pm d^{dn-d}[P(a)]^{d-1}.
\end{displaymath}">|; 

$key = q/K;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img506.png"
 ALT="$K$">|; 

$key = q/R_n(alpha)=alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img854.png"
 ALT="$R_n(\alpha) = \alpha$">|; 

$key = q/epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img308.png"
 ALT="$\epsilon$">|; 

$key = q/{displaymath}u_n=u_1+sum_1^{n-1}(u_{i+1}-u_i),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img510.png"
 ALT="\begin{displaymath}
u_n = u_1 + \sum_1^{n-1}(u_{i+1} - u_i),
\end{displaymath}">|; 

$key = q/sum_1^Ndisplaystylefrac{1}{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img550.png"
 ALT="$\sum_1^N\displaystyle\frac{1}{n}$">|; 

$key = q/left(frac{1}{d}^frac{1}{d-1}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1384.png"
 ALT="$\left( \frac{1}{d}^\frac{1}{d-1} \right)$">|; 

$key = q/{displaymath}T=(1,2)^{lambda_1}(2,3)^{lambda_2}...(d-1,d)^{lambda_{d-1}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img324.png"
 ALT="\begin{displaymath}
T = (1,2)^{\lambda_1}(2,3)^{\lambda_2}...(d-1, d)^{\lambda_{d-1}},
\end{displaymath}">|; 

$key = q/t^{frac{1}{p}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="25" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img649.png"
 ALT="$t^{\frac{1}{p}}$">|; 

$key = q/R(y)=z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1349.png"
 ALT="$R(y)=z$">|; 

$key = q/R(z)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1092.png"
 ALT="$R(z) = 0$">|; 

$key = q/(r,+infty);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img456.png"
 ALT="$(r, +\infty)$">|; 

$key = q/S(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$S(z)$">|; 

$key = q/{displaymath}R(z)=sz-a_2z^2+cdots+a_hz^h+cdots,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img783.png"
 ALT="\begin{displaymath}
R(z) = sz - a_2z^2 + \cdots + a_hz^h + \cdots,
\end{displaymath}">|; 

$key = q/gamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img300.png"
 ALT="$\gamma$">|; 

$key = q/z=f(t),z_1=f(t_1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img843.png"
 ALT="$z = f(t), z_1 = f(t_1)$">|; 

$key = q/{displaymath}array{{c}t_n=S(t_{n-1}),S(t)=t+pa+frac{b'}{t^frac{1}{p}}+frac{c'}{t^frac{2}{p}}+cdots.array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="61" BORDER="0"
 SRC="|."$dir".q|img765.png"
 ALT="\begin{displaymath}
\begin{array}{c}
t_n = S(t_{n-1}), \\\\
S(t) = t + pa + \frac...
...t^\frac{1}{p}} + \frac{c'}{t^\frac{2}{p}} + \cdots.
\end{array}\end{displaymath}">|; 

$key = q/geq2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img962.png"
 ALT="$\geq 2$">|; 

$key = q/q=p+k-h<p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$q = p + k - h &lt; p$">|; 

$key = q/displaystyleu+iv,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$\displaystyle u + iv,$">|; 

$key = q/sigma_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1109.png"
 ALT="$\sigma_{-n}$">|; 

$key = q/S10;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1026.png"
 ALT="$\S 10$">|; 

$key = q/{displaymath}C_{-k}^{(1)}C_{-k}^{(2)}dotsC_{-k}^{(3^k)}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img1196.png"
 ALT="\begin{displaymath}
C_{-k}^{(1)}C_{-k}^{(2)}\dots C_{-k}^{(3^k)}
\end{displaymath}">|; 

$key = q/e^{textstylefrac{2pipi}{q}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="32" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1125.png"
 ALT="$e^{\textstyle\frac{2pi\pi}{q}}$">|; 

$key = q/midtmidleq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$\mid t\mid \leq1$">|; 

$key = q/e^{textstylefrac{2ipim}{p}}z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="32" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img822.png"
 ALT="$e^{\textstyle\frac{2i\pi m}{p}}z$">|; 

$key = q/{displaymath}l_{-n},frac{1}{k'}l_{-(n-1)},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1204.png"
 ALT="\begin{displaymath}
l_{-n}, \frac{1}{k'}l_{-(n-1)},
\end{displaymath}">|; 

$key = q/t=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1425.png"
 ALT="$t=1$">|; 

$key = q/{displaymath}R_{q-1}(z)=overline{omega}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="\begin{displaymath}
R_{q-1}(z) = \overline{\omega}
\end{displaymath}">|; 

$key = q/{displaymath}array{{llllllllllll}sigma&sigma'&sigma&sigma'&sigma''&sigma&sigma'&igma_{-a_7}&sigma_{-a_8}&sigma_{-a_9}&dotsarray{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="513" HEIGHT="76" BORDER="0"
 SRC="|."$dir".q|img1142.png"
 ALT="\begin{displaymath}
\begin{array}{llllllllllll}
\sigma &amp; \sigma' &amp; \sigma &amp; \sig...
...gma_{-a_7} &amp; \sigma_{-a_8} &amp; \sigma_{-a_9} &amp; \dots
\end{array}\end{displaymath}">|; 

$key = q/{displaymath}F(z)=z+mbox{func.acotada}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img559.png"
 ALT="\begin{displaymath}
F(z) = z + \mbox{func. acotada}.
\end{displaymath}">|; 

$key = q/midzmid<r<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1299.png"
 ALT="$\mid z \mid &lt; r &lt; 1$">|; 

$key = q/{displaymath}sum_0^infty=sum_0^N+sum_{N+1}^infty,ø{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="60" BORDER="0"
 SRC="|."$dir".q|img578.png"
 ALT="\begin{displaymath}
\sum_0^\infty = \sum_0^N + \sum_{N+1}^\infty,Ã¸
\end{displaymath}">|; 

$key = q/displaystylesum^{d}_{1}left(-frac{1}{2}-Lright)+Releft(frac{1}{s'-1}right)+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$\displaystyle \sum^{d}_{1}\left(-\frac{1}{2} - L\right) + \Re\left(\frac{1}{s' - 1}\right) + 1$">|; 

$key = q/{displaymath}A_hs(s^{h-1}-1)=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img797.png"
 ALT="\begin{displaymath}
A_hs(s^{h-1}-1) = 0.
\end{displaymath}">|; 

$key = q/displaystyle+s^{(n-1)(q-1)}](z-alpha)^q+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$\displaystyle + s^{(n-1)(q-1)} ](z - \alpha)^q + \cdots$">|; 

$key = q/midz_1mid>kmidzmid,;(k<1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="188" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1379.png"
 ALT="$\mid z_1\mid &gt; k\mid z\mid,\; ( k &lt; 1)$">|; 

$key = q/{displaymath}f(z)=frac{1}{z}+oleft({calL}frac{1}{midzmid}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="188" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img757.png"
 ALT="\begin{displaymath}
f(z) = \frac{1}{z} + o\left({\cal L}\frac{1}{\mid z\mid}\right).
\end{displaymath}">|; 

$key = q/S2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1021.png"
 ALT="$\S 2$">|; 

$key = q/[H(z_n)]^{frac{1}{q^n}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img379.png"
 ALT="$[H(z_n)]^{\frac{1}{q^n}}$">|; 

$key = q/c,c',c'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img345.png"
 ALT="$c, c', c''$">|; 

$key = q/displaystylefrac{d^n-d}{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img912.png"
 ALT="$\displaystyle\frac{d^n - d}{n}$">|; 

$key = q/u_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img329.png"
 ALT="$u_2$">|; 

$key = q/y>t_0>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1240.png"
 ALT="$y &gt; t_0 &gt; 0$">|; 

$key = q/{C'}_{-(n-1)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1387.png"
 ALT="${C'}_{-(n-1)}$">|; 

$key = q/displaystylensum^{frac{d^n-d}{n}}_{1}frac{1}{t-1}+sum^{d+1}_{1}frac{1}{s^n-1}+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="87" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="$\displaystyle n\sum^{\frac{d^n - d}{n}}_{1}\frac{1}{t-1} + \sum^{d + 1}_{1}\frac{1}{s^n - 1} + 1$">|; 

$key = q/sigma^{(K)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1145.png"
 ALT="$\sigma^{(K)}$">|; 

$key = q/u_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img318.png"
 ALT="$u_i$">|; 

$key = q/displaystylefrac{b}{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img525.png"
 ALT="$\displaystyle\frac{b}{a}$">|; 

$key = q/{displaymath}Re(sigma)>-frac{1}{2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="\begin{displaymath}
\Re(\sigma) &gt; -\frac{1}{2}
\end{displaymath}">|; 

$key = q/1^{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img734.png"
 ALT="$1^{0}$">|; 

$key = q/f(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img824.png"
 ALT="$f(t)$">|; 

$key = q/C_{-(n-1)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1201.png"
 ALT="$C_{-(n-1)}$">|; 

$key = q/Q(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img238.png"
 ALT="$Q(z)$">|; 

$key = q/midz=alphamid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img855.png"
 ALT="$\mid z = \alpha\mid $">|; 

$key = q/R^{(1)}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1042.png"
 ALT="$R^{(1)}(z)$">|; 

$key = q/t_1=st;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img362.png"
 ALT="$t_1 = st$">|; 

$key = q/(mgeq2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1288.png"
 ALT="$(m \geq 2)$">|; 

$key = q/t';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1421.png"
 ALT="$t'$">|; 

$key = q/{displaymath}F(z)-z=lim_{n=infty}left[sum_0^{n-1}frac{b}{z_i}-frac{b}{a}{calL}n+sum_0^{n-1}chi(z_i)right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img523.png"
 ALT="\begin{displaymath}
F(z) - z = \lim_{n=\infty}\left[ \sum_0^{n-1}\frac{b}{z_i} - \frac{b}{a}{\cal L}n + \sum_0^{n-1}\chi(z_i) \right].
\end{displaymath}">|; 

$key = q/2circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img268.png"
 ALT="$2\circ$">|; 

$key = q/R(z)=A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1003.png"
 ALT="$R ( z ) = A$">|; 

$key = q/Delta:1^0R_n(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img596.png"
 ALT="$\Delta: 1^0 R_n(z)$">|; 

$key = q/pmod{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img815.png"
 ALT="$\pmod{p}$">|; 

$key = q/displaystylefrac{C}{midzmid^h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img567.png"
 ALT="$\displaystyle\frac{C}{\mid z\mid ^h}$">|; 

$key = q/{displaymath}u-1geq0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="\begin{displaymath}
u-1 \geq 0
\end{displaymath}">|; 

$key = q/{displaymath}midchi(z_n)mid<frac{K}{midz_nmid^{1+beta}}<frac{K'}{n^{1+beta}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img509.png"
 ALT="\begin{displaymath}
\mid \chi(z_n)\mid &lt; \frac{K}{\mid z_n\mid ^{1+\beta}} &lt; \frac{K'}{n^{1+\beta}}.
\end{displaymath}">|; 

$key = q/displaystylefrac{Ai}{y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img933.png"
 ALT="$\displaystyle\frac{Ai}{y}$">|; 

$key = q/m>2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1290.png"
 ALT="$ m &gt; 2$">|; 

$key = q/{calD}_1=R({calD});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1350.png"
 ALT="${\cal D}_1 = R({\cal D})$">|; 

$key = q/{displaymath}W=R_1(w),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1477.png"
 ALT="\begin{displaymath}
W = R_1(w),
\end{displaymath}">|; 

$key = q/aa_{-1},a_{-1}a_{-2},dots,a_{-n}a_{-(n+1)},dots,bb_{-1},b_{-1}b_{-2},dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="402" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1455.png"
 ALT="$aa_{-1}, a_{-1} a_{-2},\dots,
a_{-n}a_{-(n+1)}, \dots, bb_{-1},b_{-1}b_{-2}, \dots$">|; 

$key = q/R'(omega);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1458.png"
 ALT="$R'(\omega)$">|; 

$key = q/cos(mvarphi+a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1518.png"
 ALT="$\cos(m\varphi + a)$">|; 

$key = q/{displaymath}array{{cc}R(a_{-n})=a_{-(n-1)}&R(b_{-n})=b_{-(n-1)}.array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1447.png"
 ALT="\begin{displaymath}\begin{array}{cc}
R(a_{-n}) = a_{-(n-1)} &amp; R(b_{-n}) = b_{-(n-1)}.
\end{array}\end{displaymath}">|; 

$key = q/p>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img833.png"
 ALT="$p &gt; 1$">|; 

$key = q/{displaymath}sum_1^dfrac{1}{s_i-1}frac{1}{z-alpha_l}+frac{1}{z-A}-frac{1}{1-s}frac{1}{z-alpha}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="359" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1015.png"
 ALT="\begin{displaymath}
\sum_1^d\frac{1}{s_i - 1}\frac{1}{z - \alpha_l} + \frac{1}{z - A} - \frac{1}{1 - s}\frac{1}{z - \alpha} = 0.
\end{displaymath}">|; 

$key = q/frac{pi}{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img676.png"
 ALT="$\frac{\pi}{p}$">|; 

$key = q/(x>A);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img560.png"
 ALT="$(x &gt; A)$">|; 

$key = q/C_{-2}^{(4)},C_{-2}^{(5)},C_{-2}^{(6)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1192.png"
 ALT="$C_{-2}^{(4)}, C_{-2}^{(5)}, C_{-2}^{(6)}$">|; 

$key = q/z=lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1215.png"
 ALT="$z = \lambda$">|; 

$key = q/xi_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img774.png"
 ALT="$\xi_{-n}$">|; 

$key = q/2(d-1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img334.png"
 ALT="$2(d-1)$">|; 

$key = q/midR'(z)mid>K>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1110.png"
 ALT="$\mid R'(z)\mid &gt; K &gt; 1$">|; 

$key = q/displaystylefrac{1}{s-1}=xi+ieta.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\displaystyle \frac{1}{s-1} = \xi + i\eta.$">|; 

$key = q/{displaymath}left|(m-1)-displaystylefrac{2}{z^m}right|>sqrt{(m-1)^2+frac{1}{2^{2m-2}}}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="308" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img1319.png"
 ALT="\begin{displaymath}
\left\vert (m-1) - \displaystyle\frac{2}{z^m} \right\vert &gt; \sqrt{(m - 1)^2 + \frac{1}{2^{2m - 2}}}
\end{displaymath}">|; 

$key = q/x=a,y>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img932.png"
 ALT="$x = a, y &gt; 0$">|; 

$key = q/pp'+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img791.png"
 ALT="$pp' + 1$">|; 

$key = q/q-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$q-1$">|; 

$key = q/z<z_1<cdots<z_n<cdots,lim_{n=infty}z_n=+infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="344" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1216.png"
 ALT="$z &lt; z_1 &lt; \cdots &lt; z_n &lt; \cdots, \lim_{n = \infty} z_n = +\infty$">|; 

$key = q/z_n=w_n^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1497.png"
 ALT="$z_n = w_n^2$">|; 

$key = q/{displaymath}frac{pi}{2}-arg.z>arcsinfrac{midpsi(z)mid}{a}hspace{0.3in}[psi=z_1-z-a]{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="383" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img531.png"
 ALT="\begin{displaymath}
\frac{\pi}{2} - \arg .z &gt; \arcsin\frac{\mid \psi(z)\mid }{a} \hspace{0.3in} [\psi = z_1 - z - a]
\end{displaymath}">|; 

$key = q/L_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img296.png"
 ALT="$L_1$">|; 

$key = q/displaystyleX=x-sumfrac{A(x-a)}{(x-a)^2+y^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1259.png"
 ALT="$\displaystyle X = x - \sum\frac{A(x-a)}{(x-a)^2 + y^2}$">|; 

$key = q/E;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1081.png"
 ALT="$E$">|; 

$key = q/{displaymath}R(z)=frac{zlambda(z)-b^2}{z+lambda(z)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1056.png"
 ALT="\begin{displaymath}
R(z) = \frac{z\lambda(z) - b^2}{z + \lambda(z)}.
\end{displaymath}">|; 

$key = q/s=2alpha=1pmisqrt{19};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1280.png"
 ALT="$s = 2\alpha = 1 \pm i\sqrt{19}$">|; 

$key = q/Z={Large{frac{A}{z^m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img273.png"
 ALT="$Z = \Large\frac{A}{z^m}$">|; 

$key = q/z+na;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img446.png"
 ALT="$z + na$">|; 

$key = q/{z'}_{-1}=f(z');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1178.png"
 ALT="${z'}_{-1} = f(z')$">|; 

$key = q/alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$\alpha$">|; 

$key = q/D_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img900.png"
 ALT="$D_0$">|; 

$key = q/Psi(t)=frac{b'}{t^frac{1}{p}}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img766.png"
 ALT="$\Psi (t) = \frac{b'}{t^\frac{1}{p}} + \cdots$">|; 

$key = q/t=F(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img360.png"
 ALT="$ t = F(z)$">|; 

$key = q/{displaymath}mida_{-n}-a_{-(n-1)}mid<frac{A}{K^n}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1450.png"
 ALT="\begin{displaymath}
\mid a_{-n} - a_{-(n-1)}\mid &lt; \frac{A}{K^n}.
\end{displaymath}">|; 

$key = q/R^{(D)}_{-n'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img304.png"
 ALT="$R^{(D)}_{-n'}$">|; 

$key = q/{calA};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1222.png"
 ALT="${\cal A}$">|; 

$key = q/displaystylefrac{1}{(m-1)^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1322.png"
 ALT="$\displaystyle\frac{1}{(m - 1)^2}$">|; 

$key = q/a_{2p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img701.png"
 ALT="$a_{2p}$">|; 

$key = q/{displaymath}R_n(z)=sqrt{2n+f(z)+varepsilon_n},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img761.png"
 ALT="\begin{displaymath}
R_n(z) = \sqrt{2n + f(z) + \varepsilon_n},
\end{displaymath}">|; 

$key = q/Y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img608.png"
 ALT="$Y$">|; 

$key = q/{displaymath}array{{lcr}&lima_{-n}=omega,&R(omega)=omega,&&midR'(omega)mid>1.array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1452.png"
 ALT="\begin{displaymath}\begin{array}{lcr}
&amp; \lim a_{-n} = \omega, &amp; \\\\
R(\omega) = \omega, &amp; &amp; \mid R'(\omega)\mid &gt; 1.
\end{array}\end{displaymath}">|; 

$key = q/{R''}_2(z)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img993.png"
 ALT="${R''}_2(z) = 0$">|; 

$key = q/1circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img267.png"
 ALT="$1\circ$">|; 

$key = q/{displaymath}midz_nmid<c^nmidzmid,hspace{0.3in}limz_n=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1080.png"
 ALT="\begin{displaymath}
\mid z_n\mid &lt; c^n\mid z\mid , \hspace{0.3in} \lim z_n = 0
\end{displaymath}">|; 

$key = q/ik;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img320.png"
 ALT="$ik$">|; 

$key = q/{displaymath}P(n)=sum_{deltaslashn}mu(delta)left[d^{mbox{{{normalsize{frac{n}{de}mu(delta)d^{mbox{{{normalsize{frac{n}{delta}{}}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="307" HEIGHT="56" BORDER="0"
 SRC="|."$dir".q|img1129.png"
 ALT="\begin{displaymath}
P(n) = \sum_{\delta/n}\mu(\delta)\left[ d^{\mbox{$\normalsiz...
..._{\delta/n}\mu(\delta)d^{\mbox{$\normalsize\frac{n}{\delta}$}}
\end{displaymath}">|; 

$key = q/Theta_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img540.png"
 ALT="$\Theta_n$">|; 

$key = q/{displaymath}array{{c}w_n=P(z_n),hspace{0.3in}w=P(z),!!w_n=t_n^{-frac{1}{p}},hspn,p,a+frac{b}{a}{calL}n+F(t)+varepsilon_n;array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="85" BORDER="0"
 SRC="|."$dir".q|img731.png"
 ALT="\begin{displaymath}
\begin{array}{c}
w_n = P(z_n), \hspace{0.3in} w = P(z), \\\\
...
...a + \frac{b}{a} {\cal L}n + F(t) + \varepsilon_n;
\end{array}\end{displaymath}">|; 

$key = q/displaystylefrac{1}{omegat^frac{1}{p}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img725.png"
 ALT="$\displaystyle\frac{1}{\omega t^\frac{1}{p}}$">|; 

$key = q/lambdap-q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img816.png"
 ALT="$\lambda p - q$">|; 

$key = q/midz_nmid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img480.png"
 ALT="$\mid z_n\mid $">|; 

$key = q/{Large{{e^{2ipifrac{m}{r}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\Large {e^{2i\pi\frac{m}{r}}}$">|; 

$key = q/midR'(z)midgeqfrac{3}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1413.png"
 ALT="$\mid R'(z)\mid \geq \frac{3}{2}$">|; 

$key = q/w^2=a^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1468.png"
 ALT="$w^2 = a^2$">|; 

$key = q/{displaymath}frac{1}{s-1}=u+iv,hspace{0.3in}frac{1}{s'-1}=u-iv.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img966.png"
 ALT="\begin{displaymath}
\frac{1}{s-1} = u+iv, \hspace{0.3in} \frac{1}{s'-1} = u -iv.
\end{displaymath}">|; 

$key = q/{displaymath}y_{n+1}-y_n=y_nsumfrac{A}{(x_n-a)^2+n^2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1238.png"
 ALT="\begin{displaymath}
y_{n + 1} - y_n = y_n\sum\frac{A}{(x_n - a)^2 + n^2}
\end{displaymath}">|; 

$key = q/C_{-2}^{(1)},C_{-2}^{(2)},C_{-2}^{(3)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1191.png"
 ALT="$C_{-2}^{(1)}, C_{-2}^{(2)}, C_{-2}^{(3)}$">|; 

$key = q/midsmid=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$\mid s \mid = 1$">|; 

$key = q/{displaymath}R(z)=kz+h-sumfrac{A}{z-a}hspace{0.3in}(A>0,;k>1),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="374" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1159.png"
 ALT="\begin{displaymath}
R(z) = kz + h - \sum\frac{A}{z - a} \hspace{0.3in} (A &gt; 0, \;k &gt; 1),
\end{displaymath}">|; 

$key = q/{displaymath}[f(t)]=f[d.t]mbox{({d{,gradode{R{)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1461.png"
 ALT="\begin{displaymath}[f(t)]= f[d.t] \mbox{ ($d$, grado de $R$)}.
\end{displaymath}">|; 

$key = q/sneq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img354.png"
 ALT="$s \neq 0$">|; 

$key = q/xsinomega+ycosomega=rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img460.png"
 ALT="$x \sin\omega + y \cos\omega = \rho$">|; 

$key = q/{figure}vbox{include{INTRODEF}}{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="978" HEIGHT="1265" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="\begin{figure}\vbox{\include{INTRODEF}
}\end{figure}">|; 

$key = q/R_q[f_{lambdap}(z)]=R_lambda(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img818.png"
 ALT="$R_q[f_{\lambda p}(z)] = R_\lambda(z)$">|; 

$key = q/z+iy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img937.png"
 ALT="$z + iy$">|; 

$key = q/{displaymath}Z=z^2+5{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1265.png"
 ALT="\begin{displaymath}
Z = z^2 + 5
\end{displaymath}">|; 

$key = q/{displaymath}R(z)=rho+frac{1}{Q(z)},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img237.png"
 ALT="\begin{displaymath}
R(z) = \rho + \frac{1}{Q(z)},
\end{displaymath}">|; 

$key = q/omega=+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img664.png"
 ALT="$\omega = +1$">|; 

$key = q/beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img842.png"
 ALT="$\beta$">|; 

$key = q/(C_{-n},{C'}_{-n});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1431.png"
 ALT="$(C_{-n}, {C'}_{-n})$">|; 

$key = q/lambda_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img326.png"
 ALT="$\lambda_1$">|; 

$key = q/{displaymath}z_1=z+a+psi(z),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img433.png"
 ALT="\begin{displaymath}
z_1 = z + a + \psi(z),
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{R(z)-z}=frac{l}{(z-alpha)^2}+frac{h}{z-alpha}+sum^{d-1}_1frac{1}{s_i-1}frac{1}{z-alpha_i},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="408" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1022.png"
 ALT="$\displaystyle \frac{1}{R(z) - z} = \frac{l}{(z - \alpha)^2} + \frac{h}{z - \alpha} + \sum^{d-1}_1 \frac{1}{s_i - 1}\frac{1}{z - \alpha_i},$">|; 

$key = q/f(t+1)=f(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1347.png"
 ALT="$f(t +1) = f(t)$">|; 

$key = q/midz_1mid>K'midzmid;(K'>1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1378.png"
 ALT="$\mid z_1\mid &gt; K'\mid z\mid \; ( K' &gt; 1)$">|; 

$key = q/displaystyleR'(alpha_2)F_3(z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img425.png"
 ALT="$\displaystyle R'(\alpha_2)F_3(z),$">|; 

$key = q/sigma_{-a_3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1139.png"
 ALT="$\sigma_{-a_3}$">|; 

$key = q/displaystylefrac{-1+sqrt{2}}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img896.png"
 ALT="$\displaystyle\frac{-1 + \sqrt{2}}{2}$">|; 

$key = q/Z=A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1012.png"
 ALT="$Z = A$">|; 

$key = q/{displaymath}sF(z)=F[R(z)].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img860.png"
 ALT="\begin{displaymath}
sF(z) = F[R(z)].
\end{displaymath}">|; 

$key = q/R(xi);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1187.png"
 ALT="$R(\xi)$">|; 

$key = q/limz_n=infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img889.png"
 ALT="$\lim z_n = \infty$">|; 

$key = q/midR'(z)mid>K'>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1351.png"
 ALT="$\mid R'(z)\mid &gt; K' &gt; 1$">|; 

$key = q/(d+1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img980.png"
 ALT="$(d + 1)$">|; 

$key = q/h=pp'+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img802.png"
 ALT="$h = pp' + 1$">|; 

$key = q/Pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img916.png"
 ALT="$\Pi$">|; 

$key = q/{displaymath}midsmid>1{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="\begin{displaymath}
\mid s \mid &gt; 1
\end{displaymath}">|; 

$key = q/mC_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1323.png"
 ALT="$mC_{-n}$">|; 

$key = q/{displaymath}R(z)=frac{R^{(1)}(z)R^{(2)}(z)-midbetamid^2}{R^{(1)}(z)+R^{(2)}(z)-2Re(beta)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1045.png"
 ALT="\begin{displaymath}
R(z) = \frac{R^{(1)}(z)R^{(2)}(z) - \mid \beta\mid ^2}{R^{(1)}(z) + R^{(2)}(z) - 2\Re(\beta)}.
\end{displaymath}">|; 

$key = q/(alpha_1,alpha_2,dots,alpha_d,A);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1017.png"
 ALT="$(\alpha_1, \alpha_2, \dots, \alpha_d, A)$">|; 

$key = q/limy_n=infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1165.png"
 ALT="$\lim y_n= \infty$">|; 

$key = q/{displaymath}summbox{'area}C_{-n}<frac{m}{(m-1)^2}summbox{'area}C_{-(n-1)},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1325.png"
 ALT="\begin{displaymath}
\sum\mbox{\'area} C_{-n} &lt; \frac{m}{(m-1)^2}\sum\mbox{\'area} C_{-(n-1)},
\end{displaymath}">|; 

$key = q/delta_{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1101.png"
 ALT="$\delta_{-2}$">|; 

$key = q/Theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1153.png"
 ALT="$\Theta$">|; 

$key = q/Delta_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img624.png"
 ALT="$\Delta_1$">|; 

$key = q/{displaymath}R_{q-1}(z)=frac{C}{(z-rho)^k}+D,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img247.png"
 ALT="\begin{displaymath}
R_{q-1}(z) = \frac{C}{(z - \rho)^k} + D,
\end{displaymath}">|; 

$key = q/s^{q-1}=+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$s^{q-1} = +1$">|; 

$key = q/R(Z)=kiy+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img938.png"
 ALT="$R(Z) = kiy +$">|; 

$key = q/overline{omega}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img221.png"
 ALT="$\overline{\omega}'$">|; 

$key = q/omega+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img813.png"
 ALT="$\omega + $">|; 

$key = q/displaystyleu_{n+1}=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img372.png"
 ALT="$\displaystyle u_{n+1} =$">|; 

$key = q/displaystylesum^{d+1}_{1}frac{1}{s-1}+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="$\displaystyle \sum^{d + 1}_{1}\frac{1}{s-1} + 1$">|; 

$key = q/displaystylefrac{midzmid}{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img554.png"
 ALT="$\displaystyle\frac{\mid z\mid }{N}$">|; 

$key = q/midz_nmid>(a-muvarepsilon)n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img481.png"
 ALT="$\mid z_n\mid &gt; (a - \mu\varepsilon)n$">|; 

$key = q/{displaymath}w=sqrt{frac{1-z}{1+z}},hspace{0.3in}W=sqrt{frac{1-Z}{1+Z}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="56" BORDER="0"
 SRC="|."$dir".q|img1505.png"
 ALT="\begin{displaymath}
w = \sqrt{\frac{1-z}{1 + z}},\hspace{0.3in} W = \sqrt{\frac{1-Z}{1 + Z}},
\end{displaymath}">|; 

$key = q/midzmid>4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1266.png"
 ALT="$\mid z\mid &gt; 4$">|; 

$key = q/{displaymath}frac{1}{R(z)-z}=frac{1}{(s-1)(z-alpha)}+frac{1}{(s'-1)(z-alpha')}+sum_1^{d-1}frac{1}{(s_i-1)(z-alpha_i)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="552" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1001.png"
 ALT="\begin{displaymath}
\frac{1}{R(z) - z} = \frac{1}{(s -1)(z - \alpha)} + \frac{1}...
...z - \alpha')} + \sum_1^{d -1}\frac{1}{(s_i -1)(z - \alpha_i)}.
\end{displaymath}">|; 

$key = q/lambda=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$\lambda = 0$">|; 

$key = q/Q(w);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img751.png"
 ALT="$Q(w)$">|; 

$key = q/(alpha,alpha_1,dots,alpha_{p-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img409.png"
 ALT="$(\alpha, \alpha_1, \dots, \alpha_{p-1})$">|; 

$key = q/z_{4n+2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img903.png"
 ALT="$z_{4n + 2}$">|; 

$key = q/dsigma_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1106.png"
 ALT="$d\sigma_{-n}$">|; 

$key = q/displaystylefrac{R_n(z)-alpha}{s^n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img355.png"
 ALT="$\displaystyle\frac{R_n(z) - \alpha}{s^n}$">|; 

$key = q/{displaymath}dsigma_{-n}<frac{1}{K}dsigma_{-(n-1)},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1113.png"
 ALT="\begin{displaymath}
d\sigma_{-n} &lt; \frac{1}{K}d\sigma_{-(n-1)},
\end{displaymath}">|; 

$key = q/{displaymath}R(z)=frac{R^{(1)}(z)R^{(2)}(z)-b^2}{R^{(1)}(z)+R^{(2)}(z)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="224" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1047.png"
 ALT="\begin{displaymath}
R(z) = \frac{R^{(1)}(z)R^{(2)}(z) - b^2}{R^{(1)}(z) + R^{(2)}(z)}.
\end{displaymath}">|; 

$key = q/midz^m+2mid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1298.png"
 ALT="$\mid z^m + 2\mid $">|; 

$key = q/{displaymath}mbox{longitud}(a_{-n},a_{-(n-1)})<frac{A}{K^n},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1449.png"
 ALT="\begin{displaymath}
\mbox{longitud }(a_{-n}, a_{-(n-1)}) &lt; \frac{A}{K^n},
\end{displaymath}">|; 

$key = q/beta_n(s);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="$\beta_n(s)$">|; 

$key = q/{displaymath}R'(z)=k+sumfrac{A}{(z-a)^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1160.png"
 ALT="\begin{displaymath}
R'(z) = k + \sum\frac{A}{(z - a)^2}.
\end{displaymath}">|; 

$key = q/+frac{pi}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1313.png"
 ALT="$+\frac{\pi}{2}$">|; 

$key = q/z_{4n+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img902.png"
 ALT="$z_{4n + 1}$">|; 

$key = q/{displaymath}array{{rcl}R(z)&=&G(Z+a),R_n(z)&=&G(Z+na).array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img626.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
R(z) &amp; = &amp; G(Z + a), \\\\
R_n(z) &amp; = &amp; G(Z + na).
\end{array}\end{displaymath}">|; 

$key = q/a_{p+1}=a;;(aneq0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img702.png"
 ALT="$a_{p+1} = a \;\; (a \neq 0)$">|; 

$key = q/{displaymath}midR(z)-alphamid<kmidz-alphamid,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img865.png"
 ALT="\begin{displaymath}
\mid R(z) - \alpha\mid &lt; k\mid z - \alpha\mid ,
\end{displaymath}">|; 

$key = q/c_{n+p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1230.png"
 ALT="$c_{n+p}$">|; 

$key = q/D_{p-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img338.png"
 ALT="$D_{p-1}$">|; 

$key = q/omega_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img687.png"
 ALT="$\omega_1$">|; 

$key = q/{displaymath}array{{rcl}a_{p+2}+2a_{p+1}lambda_2&=&(p+1)a_{p+1}lambda_2,a_{p+3}+3,dots,lambda_{p-1})+(p+1)a_{p+1}lambda_p.array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="589" HEIGHT="132" BORDER="0"
 SRC="|."$dir".q|img697.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
a_{p+2} + 2a_{p+1}\lambda_2 &amp; = &amp; (p+1)a_...
...a_3, \dots, \lambda_{p-1}) + (p+1)a_{p+1}\lambda_p.
\end{array}\end{displaymath}">|; 

$key = q/Phi^{(1)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1038.png"
 ALT="$\Phi^{(1)}$">|; 

$key = q/z_1>z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1262.png"
 ALT="$z_1 &gt; z$">|; 

$key = q/(midtmidleq1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1511.png"
 ALT="$(\mid t\mid \leq 1)$">|; 

$key = q/alpha_1,alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1031.png"
 ALT="$\alpha_1, \alpha$">|; 

$key = q/L,L>M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1368.png"
 ALT="$L, L &gt; M$">|; 

$key = q/displaystyle-1+sum^{d}_{1}left(-frac{1}{2}right)+Sigma{L},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$\displaystyle -1 + \sum^{d}_{1}\left(-\frac{1}{2}\right) + \Sigma{L},$">|; 

$key = q/displaystyles;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\displaystyle s$">|; 

$key = q/{displaymath}t_1^frac{1}{p}=omegaR(z)=omegaz_1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img660.png"
 ALT="\begin{displaymath}
t_1^\frac{1}{p} = \omega R(z) = \omega z_1,
\end{displaymath}">|; 

$key = q/y_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img613.png"
 ALT="$y_1$">|; 

$key = q/b=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img558.png"
 ALT="$b=0$">|; 

$key = q/Phi(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img391.png"
 ALT="$\Phi(z)$">|; 

$key = q/displaystylefrac{1}{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img417.png"
 ALT="$\displaystyle\frac{1}{n}$">|; 

$key = q/z_{4n+3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img905.png"
 ALT="$z_{4n + 3}$">|; 

$key = q/{displaymath}fleft(z+frac{1}{z}right)=f(z)+2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img762.png"
 ALT="\begin{displaymath}
f\left( z + \frac{1}{z} \right) = f(z) + 2.
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{R_n(z)-z_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1354.png"
 ALT="$\displaystyle\frac{1}{R_n(z) - z_0}$">|; 

$key = q/{displaymath}R_{-1}^{(alpha_1)}left[R_{-1}^{(alpha_2)}left[R_{-1}^{(alpha_3)}[dots(z)]right]right].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img1403.png"
 ALT="\begin{displaymath}
R_{-1}^{(\alpha_1)}\left[ R_{-1}^{(\alpha_2)} \left[ R_{-1}^{(\alpha_3)}[\dots(z)]\right]\right].
\end{displaymath}">|; 

$key = q/{displaymath}frac{1}{s-1}+sum_1^dfrac{1}{s_i-1}+1=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1014.png"
 ALT="\begin{displaymath}
\frac{1}{s - 1} + \sum_1^d\frac{1}{s_i - 1} + 1 = 0
\end{displaymath}">|; 

$key = q/lambda'(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1067.png"
 ALT="$\lambda'(z) $">|; 

$key = q/p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$p$">|; 

$key = q/z_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$z_{-n}$">|; 

$key = q/3circ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img272.png"
 ALT="$3\circ$">|; 

$key = q/A>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img936.png"
 ALT="$A &gt; 0$">|; 

$key = q/{displaymath}R_p[R(z)]=R[R_p(z)],{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img792.png"
 ALT="\begin{displaymath}
R_p[R(z)] = R[R_p(z)],
\end{displaymath}">|; 

$key = q/w_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img737.png"
 ALT="$w_n$">|; 

$key = q/alpha^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1498.png"
 ALT="$\alpha^2$">|; 

$key = q/y;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img609.png"
 ALT="$y$">|; 

$key = q/Delta^{(1)},Delta^{(2)},dots,Delta^{(p)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img719.png"
 ALT="$ \Delta^{(1)},\Delta^{(2)}, \dots, \Delta^{(p)}$">|; 

$key = q/z=x+iy;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img930.png"
 ALT="$z = x + iy$">|; 

$key = q/{displaymath}varphi(z)=frac{1}{R(z)-z}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="\begin{displaymath}
\varphi(z) = \frac{1}{R(z) - z}.
\end{displaymath}">|; 

$key = q/z^3=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1330.png"
 ALT="$z^3 = $">|; 

$key = q/(a',lambda);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1254.png"
 ALT="$(a', \lambda)$">|; 

$key = q/{displaymath}-A<sum^{d+1}_{1}Releft(frac{1}{s^n-1}right)+1<+A,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="\begin{displaymath}
-A &lt; \sum^{d + 1}_{1}\Re\left(\frac{1}{s^n - 1}\right) + 1 &lt; + A,
\end{displaymath}">|; 

$key = q/R''(alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img431.png"
 ALT="$R''(\alpha)$">|; 

$key = q/Delta(x>A);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img595.png"
 ALT="$\Delta(x &gt; A)$">|; 

$key = q/textstyle=R_q[R_p(a_{-p})]=R_q(a).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="$\textstyle = R_q[R_p(a_{-p})] = R_q(a).$">|; 

$key = q/{displaymath}1-frac{C'}{midzmid^h}<midR'(z)mid<1+frac{C}{midzmid^h}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="271" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img569.png"
 ALT="\begin{displaymath}
1 - \frac{C'}{\mid z\mid ^h} &lt; \mid R'(z)\mid &lt; 1 + \frac{C}{\mid z\mid ^h}.
\end{displaymath}">|; 

$key = q/[zmidR_{-1}(z)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img858.png"
 ALT="$[z \mid R_{-1}(z)]$">|; 

$key = q/sigma,sigma',sigma'',dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1134.png"
 ALT="$\sigma, \sigma', \sigma'', \dots$">|; 

$key = q/t_1^frac{1}{p}=z_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img665.png"
 ALT="$t_1^\frac{1}{p} = z_1$">|; 

$key = q/displaystylefrac{1+isqrt{19}}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img882.png"
 ALT="$\displaystyle\frac{1 + i\sqrt{19}}{2}$">|; 

$key = q/I(z)geq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img920.png"
 ALT="$I(z) \geq 0$">|; 

$key = q/R(z)=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1286.png"
 ALT="$R(z) = $">|; 

$key = q/(C',{C'}_{-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1441.png"
 ALT="$(C', {C'}_{-1})$">|; 

$key = q/{displaymath}y_{n+1}>y_n>dots,>y>0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1236.png"
 ALT="\begin{displaymath}
y_{n+1} &gt; y_n &gt; \dots, &gt; y &gt; 0,
\end{displaymath}">|; 

$key = q/R_{p-1}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img820.png"
 ALT="$ R_{p-1}(z)$">|; 

$key = q/z_{-n}=R_{-n}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$z_{-n} = R_{-n}(z)$">|; 

$key = q/X;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img604.png"
 ALT="$X$">|; 

$key = q/2alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img885.png"
 ALT="$2\alpha$">|; 

$key = q/{displaymath}R(z)=alpha+s(z-alpha)+()(z-alpha)^2+cdotshspace{0.25in}(midsmid<1).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="433" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img350.png"
 ALT="\begin{displaymath}
R(z) = \alpha + s(z-\alpha) + ()(z-\alpha)^2 + \cdots \hspace{0.25in}
(\mid s\mid &lt; 1).
\end{displaymath}">|; 

$key = q/midz_{lambda+mu}-alphamid>rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img870.png"
 ALT="$\mid z_{\lambda + \mu} - \alpha\mid &gt; \rho$">|; 

$key = q/F_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img698.png"
 ALT="$F_k$">|; 

$key = q/h>k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$h &gt; k$">|; 

$key = q/-c^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1499.png"
 ALT="$-c^2$">|; 

$key = q/R(z),R_2(z),dots,R_{p-1}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img808.png"
 ALT="$R(z), R_2(z), \dots, R_{p-1}(z)$">|; 

$key = q/{displaymath}nsum^{frac{d^n-d}{n}}_{1}Releft(frac{1}{t-1}right)<-left(frac{d^n-d}{2}right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="67" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="\begin{displaymath}
n\sum^{\frac{d^n - d}{n}}_{1}\Re\left(\frac{1}{t-1}\right) &lt; - \left(\frac{d^n - d}{2}\right)
\end{displaymath}">|; 

$key = q/displaystylek=lim_{z=infty}frac{R(z)}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img929.png"
 ALT="$\displaystyle k = \lim_{z = \infty}\frac{R(z)}{z}$">|; 

$key = q/{displaymath}midA_0midx^d-midA_1midx^{d-1}-dots-[midA_{d-1}mid+1]x-midtmid=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="431" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1361.png"
 ALT="\begin{displaymath}
\mid A_0\mid x^d - \mid A_1\mid x^{d-1} - \dots - [\mid A_{d-1}\mid + 1]x - \mid t\mid = 0
\end{displaymath}">|; 

$key = q/{displaymath}t=ivarphi,hspace{0.3in}T=e^{i(mvarphi+a)}=e^{ivarphi},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1513.png"
 ALT="\begin{displaymath}
t = i\varphi, \hspace{0.3in} T = e^{i(m\varphi + a)} = e^{i\varphi},
\end{displaymath}">|; 

$key = q/alpha,alpha_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1032.png"
 ALT="$\alpha, \alpha_2$">|; 

$key = q/{displaymath}R_n(z)-na-frac{b}{a}{calL}n;{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img515.png"
 ALT="\begin{displaymath}
R_n(z) - na - \frac{b}{a}{\cal L}n;
\end{displaymath}">|; 

$key = q/midzmid<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1295.png"
 ALT="$\mid z\mid &lt; 1$">|; 

$key = q/midzmid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img547.png"
 ALT="$\mid z\mid $">|; 

$key = q/C_{-n}^{(i)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1207.png"
 ALT="$C_{-n}^{(i)}$">|; 

$key = q/{displaymath}lambda+az^q+bz^{q+h}+cdots=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="\begin{displaymath}
\lambda + az^q + bz^{q+h} + \cdots = 0
\end{displaymath}">|; 

$key = q/w_1=R_1(w),dots,w_n=R_1(w_{n-1}),dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1496.png"
 ALT="$w_1 = R_1(w),\dots, w_n = R_1(w_{n-1}), \dots$">|; 

$key = q/W=sqrt{Z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1463.png"
 ALT="$W = \sqrt{Z}$">|; 

$key = q/z^m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1312.png"
 ALT="$z^m$">|; 

$key = q/H(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img376.png"
 ALT="$H(z)$">|; 

$key = q/O;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img437.png"
 ALT="$O$">|; 

$key = q/E'=Pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1158.png"
 ALT="$E' = \Pi$">|; 

$key = q/E'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img863.png"
 ALT="$E''$">|; 

$key = q/Delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img317.png"
 ALT="$\Delta$">|; 

$key = q/{bf{4^0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img986.png"
 ALT="$\bf 4^0$">|; 

$key = q/D=D_p,D_1=D_{p+1},...;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img336.png"
 ALT="$D = D_p,
D_1 = D_{p+1}, ...$">|; 

$key = q/{displaymath}W=kw+h-sumfrac{A}{w-a},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1479.png"
 ALT="\begin{displaymath}
W = kw + h - \sum\frac{A}{w-a},
\end{displaymath}">|; 

$key = q/{displaymath}z_n=frac{1}{sqrt[textstylep]{n,p,a+o(n^{1-frac{1}{p}})}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="59" BORDER="0"
 SRC="|."$dir".q|img679.png"
 ALT="\begin{displaymath}
z_n = \frac{1}{\sqrt[\textstyle p]{n p a + o(n^{1-\frac{1}{p}})}}.
\end{displaymath}">|; 

$key = q/Z=Az^m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img269.png"
 ALT="$Z = Az^m$">|; 

$key = q/w=P(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img705.png"
 ALT="$w = P(z)$">|; 

$key = q/{displaymath}midpsi(z)mid<frac{C}{midzmid^gamma}hspace{0.3in}(C,gamma:mbox{constantespositivas}){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="390" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img435.png"
 ALT="\begin{displaymath}
\mid \psi(z)\mid &lt; \frac{C}{\mid z\mid ^\gamma} \hspace{0.3in} (C, \gamma: \mbox{ constantes positivas})
\end{displaymath}">|; 

$key = q/{displaymath}R(z)=z+az^q+bz^{q+h}+cdots{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="\begin{displaymath}
R(z) = z + az^q + bz^{q+h} + \cdots
\end{displaymath}">|; 

$key = q/mid{w}mid<frac{1}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img385.png"
 ALT="$\mid {w}\mid &lt; \frac{1}{2}$">|; 

$key = q/R(z)=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img312.png"
 ALT="$R(z) = a$">|; 

$key = q/displaystylefrac{1pmisqrt{19}}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1279.png"
 ALT="$ \displaystyle\frac{1 \pm i\sqrt{19}}{2}$">|; 

$key = q/z_{lambda+mu};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img869.png"
 ALT="$z_{\lambda + \mu}$">|; 

$key = q/{calA}_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1225.png"
 ALT="${\cal A}_p$">|; 

$key = q/{displaymath}R_p(z)=z+A_hz^h+A_{h+1}z^{h+1}+cdots.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="295" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img787.png"
 ALT="\begin{displaymath}
R_p(z) = z + A_hz^h + A_{h+1}z^{h+1} + \cdots.
\end{displaymath}">|; 

$key = q/K';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img507.png"
 ALT="$K'$">|; 

$key = q/{displaymath}4sum^{frac{d^2-d}{2}}_{1}Releft(frac{1}{t-1}right)+sum^{d+1}_{1}Releft(frac{1}{-s-1}right)+1=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="349" HEIGHT="69" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="\begin{displaymath}
4\sum^{\frac{d^2-d}{2}}_{1}\Re\left(\frac{1}{t-1}\right) + \sum^{d + 1}_{1}\Re\left(\frac{1}{-s-1}\right) + 1 = 0
\end{displaymath}">|; 

$key = q/{displaymath}w_1=w+A_{p+1}w^{p+1}+A_{2p+1}w^{2p+1}+cdots,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="328" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img690.png"
 ALT="\begin{displaymath}
w_1 = w + A_{p+1}w^{p+1} +A_{2p+1}w^{2p+1} + \cdots,
\end{displaymath}">|; 

$key = q/F(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img356.png"
 ALT="$F(z)$">|; 

$key = q/epsilon_{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img311.png"
 ALT="$\epsilon_{-1}$">|; 

$key = q/Z=X+iY;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img940.png"
 ALT="$Z = X + iY$">|; 

$key = q/z=-r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img438.png"
 ALT="$z = -r$">|; 

$key = q/t_1=[R(z)]^p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img656.png"
 ALT="$t_1 = [R(z)]^p$">|; 

$key = q/displaystylefrac{Npi}{q-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img406.png"
 ALT="$\displaystyle
\frac{N\pi}{q-1}$">|; 

$key = q/{displaymath}z_{n+1}=z_n+a+frac{b}{z_n}+chi(z_n),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img501.png"
 ALT="\begin{displaymath}
z_{n+1} = z_n + a + \frac{b}{z_n} + \chi(z_n),
\end{displaymath}">|; 

$key = q/1pmsqrt{6};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img893.png"
 ALT="$1 \pm \sqrt{6}$">|; 

$key = q/{displaymath}z_1=R(z),hspace{0.5in}z_n=R(z_{n-1}),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="\begin{displaymath}
z_1 = R(z), \hspace{0.5in} z_n = R(z_{n-1}),
\end{displaymath}">|; 

$key = q/pp';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img804.png"
 ALT="$pp'$">|; 

$key = q/Z=R_{q-1}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img229.png"
 ALT="$Z = R_{q-1}(z)$">|; 

$key = q/{displaymath}s=R'(alpha)=+1,hspace{0.3in}R''(alpha)neq0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1020.png"
 ALT="\begin{displaymath}
s = R'(\alpha) = +1, \hspace{0.3in} R''(\alpha) \neq 0
\end{displaymath}">|; 

$key = q/s>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1019.png"
 ALT="$s&gt;0$">|; 

$key = q/+3frac{pi}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1314.png"
 ALT="$+3\frac{\pi}{2}$">|; 

$key = q/R''(alpha)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img988.png"
 ALT="$R''(\alpha) = 0$">|; 

$key = q/Phi_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img699.png"
 ALT="$\Phi_k$">|; 

$key = q/displaystylefrac{1}{sqrt{n,a,p+frac{b}{a}{calL}n+C(z)+varepsilon_n}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img739.png"
 ALT="$\displaystyle\frac{1}{\sqrt{n a p + \frac{b}{a} {\cal L}n + C(z) + \varepsilon_n}}$">|; 

$key = q/displaystylefrac{pi}{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img653.png"
 ALT="$\displaystyle\frac{\pi}{p}$">|; 

$key = q/{displaymath}S(z)=inftyhspace{0.5in}{mboxy}hspace{0.5in}z=infty.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img216.png"
 ALT="\begin{displaymath}
S(z) = \infty \hspace{0.5in}{\mbox y}\hspace{0.5in} z = \infty.
\end{displaymath}">|; 

$key = q/<;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img484.png"
 ALT="$ &lt; $">|; 

$key = q/{displaymath}frac{1}{n}-{calL}left(1+frac{1}{n}right)=frac{1}{2n^2}-frac{1}{3n^3}+cdots=frac{lambda_n}{2n^2}(limlambda_n=1){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="435" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img503.png"
 ALT="\begin{displaymath}
\frac{1}{n} - {\cal L}\left(1+\frac{1}{n}\right) = \frac{1}{...
...1}{3n^3} + \cdots = \frac{\lambda_n}{2n^2}(\lim \lambda_n = 1)
\end{displaymath}">|; 

$key = q/d>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$d&gt;1$">|; 

$key = q/alpha,beta,gamma,dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1157.png"
 ALT="$\alpha, \beta, \gamma, \dots$">|; 

$key = q/z^p=t,z_n^p=t_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img764.png"
 ALT="$z^p = t, z_n^p = t_n$">|; 

$key = q/R(z)=z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$R(z) = z$">|; 

$key = q/delta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img410.png"
 ALT="$\delta$">|; 

$key = q/{displaymath}4sum^{frac{d^2-d}{2}}_{1}frac{1}{t-1}+sum^{d+1}_{1}frac{1}{-s-1}+1=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="69" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="\begin{displaymath}
4\sum^{\frac{d^2-d}{2}}_{1}\frac{1}{t-1} + \sum^{d+1}_{1}\frac{1}{-s-1} + 1 = 0.
\end{displaymath}">|; 

$key = q/Gamma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img436.png"
 ALT="$\Gamma$">|; 

$key = q/z<mu,z>z_1>z_2dots>z_ndots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1217.png"
 ALT="$z &lt; \mu, z &gt; z_1 &gt; z_2 \dots &gt; z_n \dots$">|; 

$key = q/z=displaystylesqrt[p]{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img673.png"
 ALT="$z = \displaystyle\sqrt[p]{t}$">|; 

$key = q/z=overline{omega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img266.png"
 ALT="$z = \overline{\omega}$">|; 

$key = q/{displaymath}R[R_{q-1}(z)]=S(z)=mbox{polinomioen}hspace{0.2cm}z,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="\begin{displaymath}
R[R_{q-1}(z)] = S(z) = \mbox{ polinomio en }\hspace{0.2cm} z,
\end{displaymath}">|; 

$key = q/1-epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img309.png"
 ALT="$1-\epsilon$">|; 

$key = q/{displaymath}frac{-1}{Z-alpha}=T,hspace{0.3in}frac{-1}{z-alpha}=t,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img943.png"
 ALT="\begin{displaymath}
\frac{-1}{Z-\alpha} = T, \hspace{0.3in} \frac{-1}{z - \alpha} = t,
\end{displaymath}">|; 

$key = q/{displaymath}sinomega=frac{C}{a}frac{1}{rho^gamma}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img459.png"
 ALT="\begin{displaymath}
\sin \omega = \frac{C}{a} \frac{1}{\rho^\gamma}.
\end{displaymath}">|; 

$key = q/midR'(z)mid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1332.png"
 ALT="$\mid R' ( z)\mid $">|; 

$key = q/m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img785.png"
 ALT="$m$">|; 

$key = q/=Z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1301.png"
 ALT="$ = Z$">|; 

$key = q/{displaymath}R_{-1}=sqrt{z-5}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1267.png"
 ALT="\begin{displaymath}
R_{-1} = \sqrt{z - 5}
\end{displaymath}">|; 

$key = q/{displaymath}frac{partialQ}{partialy}(A,y_3)=0=frac{partialP}{partialx}(A,y_3),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img615.png"
 ALT="\begin{displaymath}
\frac{\partial Q}{\partial y}(A, y_3) = 0 = \frac{\partial P}{\partial x}(A, y_3),
\end{displaymath}">|; 

$key = q/k=h=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img259.png"
 ALT="$k = h = 1$">|; 

$key = q/displaystyleA=lim_{z=a}R(z)(z-a),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img928.png"
 ALT="$\displaystyle A = \lim_{z = a}R(z)(z-a),$">|; 

$key = q/R^{(D)}_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img303.png"
 ALT="$R^{(D)}_{-n}$">|; 

$key = q/Q_n(w);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img720.png"
 ALT="$Q_n(w)$">|; 

$key = q/displaystylefrac{A'}{w+a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1486.png"
 ALT="$\displaystyle\frac{A'}{w + a}$">|; 

$key = q/sumdisplaystylefrac{A}{b^2+h^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1073.png"
 ALT="$\sum\displaystyle\frac{A}{b^2 + h^2}$">|; 

$key = q/(C,C');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1389.png"
 ALT="$(C, C')$">|; 

$key = q/P(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1510.png"
 ALT="$P(t)$">|; 

$key = q/Z=R_{-n}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1283.png"
 ALT="$Z = R_{-n}(z)$">|; 

$key = q/R_q(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="$R_q(z)$">|; 

$key = q/gamma=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img495.png"
 ALT="$\gamma = 1$">|; 

$key = q/displaystylefrac{A}{C^h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img260.png"
 ALT="$\displaystyle \frac{A}{C^h}$">|; 

$key = q/midamid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1285.png"
 ALT="$\mid a\mid $">|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img323.png"
 ALT="$T$">|; 

$key = q/{displaymath}R_{p-h}(alpha_h)=R_{p-h}(alpha_k),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="\begin{displaymath}
R_{p-h}(\alpha_h) = R_{p-h}(\alpha_k),
\end{displaymath}">|; 

$key = q/{Large{frac{1}{R_{q-1}(z)-overline{omega}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img217.png"
 ALT="$\Large\frac{1}{R_{q-1}(z) - \overline{\omega}}$">|; 

$key = q/{displaymath}frac{dy}{dx}=displaystylefrac{-frac{partialQ}{partialx}}{frac{parti{partialQ}{partialx}}{frac{partialP}{partialx}};{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="61" BORDER="0"
 SRC="|."$dir".q|img619.png"
 ALT="\begin{displaymath}
\frac{dy}{dx} = \displaystyle\frac{-\frac{\partial Q}{\parti...
...c{\partial Q}{\partial x}}{  \frac{\partial P}{\partial x}};
\end{displaymath}">|; 

$key = q/{bf{3^0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img983.png"
 ALT="$\bf 3^0$">|; 

$key = q/{displaymath}z_n=z+na+Theta_n{calL}n,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img539.png"
 ALT="\begin{displaymath}
z_n = z + na + \Theta_n{\cal L}n,
\end{displaymath}">|; 

$key = q/z^m=-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1291.png"
 ALT="$z^m = -1$">|; 

$key = q/alpha'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img973.png"
 ALT="$\alpha''$">|; 

$key = q/A_hsneq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img798.png"
 ALT="$A_hs \neq 0$">|; 

$key = q/{displaymath}array{{rcl}F[R(z)]&=&F(z)+a,F'[R(z)]&=&frac{1}{R'(z)}F'(z)array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="56" BORDER="0"
 SRC="|."$dir".q|img589.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
F[R(z)] &amp; = &amp; F(z) + a, \\\\
F'[R(z)] &amp; = &amp; \frac{1}{R'(z)} F'(z)
\end{array}\end{displaymath}">|; 

$key = q/sigma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$\sigma$">|; 

$key = q/D^{(1)},D^{(2)},dots,D^{(p)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img718.png"
 ALT="$D^{(1)}, D^{(2)}, \dots, D^{(p)}$">|; 

$key = q/s=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img405.png"
 ALT="$s=0$">|; 

$key = q/{displaymath}R_p(alpha)=R_{p-h+k}(alpha),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="\begin{displaymath}
R_p(\alpha) = R_{p-h+k}(\alpha),
\end{displaymath}">|; 

$key = q/z-rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img248.png"
 ALT="$z- \rho$">|; 

$key = q/{displaymath}f(z)-f(z')=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1182.png"
 ALT="\begin{displaymath}
f(z) - f(z') = 0.
\end{displaymath}">|; 

$key = q/b>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1006.png"
 ALT="$b&gt;0$">|; 

$key = q/C';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img556.png"
 ALT="$C'$">|; 

$key = q/displaystylefrac{Phi(t)}{t};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1048.png"
 ALT="$\displaystyle\frac{\Phi(t)}{t}$">|; 

$key = q/t^frac{1}{p},t_1^frac{1}{p},dots,t_n^frac{1}{p},dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img667.png"
 ALT="$t^\frac{1}{p}, t_1^\frac{1}{p},\dots,t_n^\frac{1}{p},\dots$">|; 

$key = q/-pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img650.png"
 ALT="$-\pi$">|; 

$key = q/eta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1171.png"
 ALT="$\eta$">|; 

$key = q/n^{1-gamma};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img496.png"
 ALT="$n^{1-\gamma}$">|; 

$key = q/p,q,dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img563.png"
 ALT="$p, q, \dots$">|; 

$key = q/R^{(D)}_{-n}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img306.png"
 ALT="$R^{(D)}_{-n}(z)$">|; 

$key = q/displaystyleF_{p-1}[R(z)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img426.png"
 ALT="$\displaystyle F_{p-1}[R(z)]$">|; 

$key = q/{displaymath}beta_{n}(s)=frac{1}{s^n-1}-frac{1}{n}frac{1}{s-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="\begin{displaymath}
\beta_{n}(s) = \frac{1}{s^n - 1} - \frac{1}{n}\frac{1}{s-1}.
\end{displaymath}">|; 

$key = q/midz_nmid>Kn;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img544.png"
 ALT="$\mid z_n\mid &gt; Kn$">|; 

$key = q/c,R(c),...,R_{n-2}(c),R_{n-1}(c);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img286.png"
 ALT="$c, R(c), ..., R_{n-2}(c), R_{n-1}(c)$">|; 

$key = q/[zmidR(z)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$[ z \mid R(z)]$">|; 

$key = q/S_n(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img712.png"
 ALT="$S_n(t)$">|; 

$key = q/displaystylefrac{1+dzeta^{d-1}}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1382.png"
 ALT="$\displaystyle\frac{1 + d\zeta^{d-1}}{2}$">|; 

$key = q/2beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img886.png"
 ALT="$2\beta$">|; 

$key = q/z-z_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img922.png"
 ALT="$z-z_0$">|; 

$key = q/K>d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1374.png"
 ALT="$K &gt; d$">|; 

$key = q/Psi(t)=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1051.png"
 ALT="$\Psi(t) =$">|; 

$key = q/C_{-1}^{(1)},C_{-1}^{(2)},C_{-1}^{(3)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1188.png"
 ALT="$C_{-1}^{(1)}, C_{-1}^{(2)},C_{-1}^{(3)}$">|; 

$key = q/{displaymath}R(z)=h-sum_1^dfrac{A}{z-a}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img944.png"
 ALT="\begin{displaymath}
R(z) = h - \sum_1^d\frac{A}{z-a}
\end{displaymath}">|; 

$key = q/t=s^lambdat_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img403.png"
 ALT="$t = s^\lambda t_0$">|; 

$key = q/-infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img610.png"
 ALT="$-\infty$">|; 

$key = q/textstyle[R_n(z)]^{frac{1}{q^n}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img370.png"
 ALT="$\textstyle [R_n(z)]^{\frac{1}{q^n}}$">|; 

$key = q/D;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img246.png"
 ALT="$D$">|; 

$key = q/{displaymath}z_1-alpha=z-alpha+k(z-alpha)^{q+1}+...hspace{0.5in}(kneq0){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="393" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="\begin{displaymath}
z_1 - \alpha = z - \alpha + k(z - \alpha)^{q+1} + ... \hspace{0.5in} (k \neq 0)
\end{displaymath}">|; 

$key = q/R(z)-a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img313.png"
 ALT="$R(z) - a$">|; 

$key = q/R(z)=c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img277.png"
 ALT="$R(z) = c$">|; 

$key = q/lambda_2,lambda_3,dots,lambda_{k-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img700.png"
 ALT="$\lambda_2, \lambda_3, \dots, \lambda_{k-1}$">|; 

$key = q/{displaymath}S_{p+q-1}(a_{-p})=S_{q-1}[S_p(a_{-p})]=S_{q-1}(a)=a,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="\begin{displaymath}
S_{p+q-1}(a_{-p}) = S_{q-1}[S_p(a_{-p})] = S_{q-1}(a) = a,
\end{displaymath}">|; 

$key = q/{displaymath}R_n[R_{n'}(z)]=R_{n+n'}(z),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img627.png"
 ALT="\begin{displaymath}
R_n[R_{n'}(z)] = R_{n + n'}(z),
\end{displaymath}">|; 

$key = q/z,z_1,dots,z_{n-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img849.png"
 ALT="$z, z_1, \dots, z_{n-1}$">|; 

$key = q/{displaymath}midR'(z)mid<k'<1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1200.png"
 ALT="\begin{displaymath}
\mid R'(z)\mid &lt; k' &lt; 1.
\end{displaymath}">|; 

$key = q/displaystylefrac{3pi}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1335.png"
 ALT="$\displaystyle\frac{3\pi}{2}$">|; 

$key = q/midz_{n+1}mid>midz_nmid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img529.png"
 ALT="$\mid z_{n+1}\mid &gt; \mid z_n\mid $">|; 

$key = q/z_n=R_n(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img672.png"
 ALT="$z_n = R_n(z)$">|; 

$key = q/R_{-1}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img275.png"
 ALT="$R_{-1}(z)$">|; 

$key = q/displaystyleR_{p+q}(a_{-p});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="$\displaystyle R_{p+q}(a_{-p})$">|; 

$key = q/R^u(alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1027.png"
 ALT="$R^u(\alpha)$">|; 

$key = q/Z=z^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1150.png"
 ALT="$Z = z^3$">|; 

$key = q/y_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1237.png"
 ALT="$y_n$">|; 

$key = q/{displaymath}z_1=z-az^{p+1}+cdots.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img642.png"
 ALT="\begin{displaymath}
z_1 = z - az^{p+1} + \cdots .
\end{displaymath}">|; 

$key = q/displaystyleReleft(frac{1}{s'-1}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="$\displaystyle \Re\left(\frac{1}{s' - 1}\right)$">|; 

$key = q/{displaymath}R(z)=z+frac{a}{z^{p-1}}+frac{b}{z^p}+cdotshspace{0.3in}(ambox{realpositiva}){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="390" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img763.png"
 ALT="\begin{displaymath}
R(z) = z + \frac{a}{z^{p-1}} + \frac{b}{z^p} + \cdots \hspace{0.3in} (a \mbox{ real positiva})
\end{displaymath}">|; 

$key = q/displaystyle4sum^{frac{d^2+d}{3}}_{1}Releft(frac{1}{t-1}right)+sum_{1}Releft(frac{1}{-s-1}right)+Releft(frac{1}{-s'-1}right)+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="446" HEIGHT="91" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$\displaystyle 4\sum^{\frac{d^2 + d}{3}}_{1}\Re\left(\frac{1}{t-1}\right) + \sum_{1}\Re\left(\frac{1}{-s-1}\right) + \Re\left(\frac{1}{-s' -1}\right) + 1$">|; 

$key = q/framebox[0.75in]{{-inftyhspace{0.1in}+infty{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img951.png"
 ALT="\framebox[0.75in]{$-\infty \hspace{0.1in} +\infty$}">|; 

$key = q/displaystyleR_n(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$\displaystyle R_n(z)$">|; 

$key = q/3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$3$">|; 

$key = q/sum_1^Ndisplaystylefrac{1}{na};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img548.png"
 ALT="$\sum_1^N\displaystyle\frac{1}{na}$">|; 

$key = q/gamma_{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1093.png"
 ALT="$\gamma_{-1}$">|; 

$key = q/midpsi(z)mid<;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img533.png"
 ALT="$\mid \psi(z)\mid &lt;$">|; 

$key = q/R'(alpha)R'(beta)=4alphabeta=-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img895.png"
 ALT="$R'(\alpha)R'(\beta) = 4\alpha\beta = -1$">|; 

$key = q/f(0)=0,f'(0)neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="157" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img844.png"
 ALT="$f(0)=0, f'(0) \neq 0$">|; 

$key = q/displaystylefrac{C'}{midzmid^h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img568.png"
 ALT="$\displaystyle\frac{C'}{\mid z\mid ^h}$">|; 

$key = q/2qpi;;(qgeq1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img923.png"
 ALT="$2q\pi\;\;(q \geq 1)$">|; 

$key = q/{displaymath}midxi^{(p)}mid>K>0;{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1089.png"
 ALT="\begin{displaymath}
\mid \xi^{(p)}\mid &gt; K &gt; 0;
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{t_n^frac{1}{p}}-frac{1}{(t_n+varepsilon_n)^frac{1}{p}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img742.png"
 ALT="$\displaystyle\frac{1}{t_n^\frac{1}{p}} - \frac{1}{(t_n + \varepsilon_n)^\frac{1}{p}}$">|; 

$key = q/beta_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1252.png"
 ALT="$\beta_n$">|; 

$key = q/displaystylerho.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img263.png"
 ALT="$\displaystyle \rho.$">|; 

$key = q/t_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img671.png"
 ALT="$t_n$">|; 

$key = q/displaystyleY=yleft[1+sumfrac{A}{(x-a)^2+y^2}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1260.png"
 ALT="$\displaystyle Y = y\left[ 1 + \sum\frac{A}{(x-a)^2 + y^2} \right]$">|; 

$key = q/(mgeq3);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1327.png"
 ALT="$(m \geq 3)$">|; 

$key = q/{displaymath}R(z)=frac{A}{(z-overline{omega})^h}+B,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img226.png"
 ALT="\begin{displaymath}
R(z) = \frac{A}{(z - \overline{\omega})^h} + B,
\end{displaymath}">|; 

$key = q/{displaymath}q+q'+q''+cdots,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="\begin{displaymath}
q + q' + q'' + \cdots,
\end{displaymath}">|; 

$key = q/{displaymath}z_1=R(z)=z-az^2+bz^3+cdots,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img631.png"
 ALT="\begin{displaymath}
z_1 = R(z) = z - az^2 + bz^3 + \cdots,
\end{displaymath}">|; 

$key = q/s=R'(alpha)=+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img984.png"
 ALT="$s = R'(\alpha) = + 1$">|; 

$key = q/{displaymath}midR'(z)mid>k>1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1269.png"
 ALT="\begin{displaymath}
\mid R'(z)\mid &gt; k &gt; 1.
\end{displaymath}">|; 

$key = q/Phi(t)=Phi^{(1)}Phi^{(2)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1044.png"
 ALT="$\Phi(t) = \Phi^{(1)}\Phi^{(2)}$">|; 

$key = q/a_{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$a_{-1}$">|; 

$key = q/{displaymath}sum_1^{d-1}frac{1}{(s_i-1)(z-alpha_i)}+frac{1}{z-A}+Phi(z)=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="330" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1004.png"
 ALT="\begin{displaymath}
\sum_1^{d -1}\frac{1}{(s_i -1)(z - \alpha_i)} + \frac{1}{z - A} + \Phi(z) = 0,
\end{displaymath}">|; 

$key = q/a';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1246.png"
 ALT="$a'$">|; 

$key = q/mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img439.png"
 ALT="$\mu$">|; 

$key = q/{Large{lambda^{frac{1}{q}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="25" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="$\Large\lambda^{\frac{1}{q}}$">|; 

$key = q/{displaymath}frac{u_{n+1}}{u_n}=left[frac{1}{z_n}R^{frac{1}{q}}(z_n)right]^{frac{1}{q^n}}=[H(z_n)]^{frac{1}{q^n}}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img375.png"
 ALT="\begin{displaymath}
\frac{u_{n+1}}{u_n} = \left[\frac{1}{z_n}R^{\frac{1}{q}}(z_n)\right]^{\frac{1}{q^n}} = [H(z_n)]^{\frac{1}{q^n}}
\end{displaymath}">|; 

$key = q/{displaymath}R_n(xi_{-n})=xineq0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img775.png"
 ALT="\begin{displaymath}
R_n(\xi_{-n}) = \xi \neq 0,
\end{displaymath}">|; 

$key = q/z',z'',dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1083.png"
 ALT="$z', z'', \dots$">|; 

$key = q/midz'midleqrho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img810.png"
 ALT="$\mid z' \mid \leq \rho$">|; 

$key = q/t;(0<t<1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1430.png"
 ALT="$t\; (0&lt;t&lt;1)$">|; 

$key = q/displaystyleu_n=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img369.png"
 ALT="$\displaystyle u_n =$">|; 

$key = q/{displaymath}nsum{frac{1}{t-1}}+sumfrac{1}{s^n-1}+1=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="258" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="\begin{displaymath}
n\sum{\frac{1}{t-1}} + \sum\frac{1}{s^n - 1} + 1 = 0,
\end{displaymath}">|; 

$key = q/z=G(Z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img623.png"
 ALT="$z = G(Z)$">|; 

$key = q/na;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img494.png"
 ALT="$na$">|; 

$key = q/{displaymath}array{{rcl}R(z)+lambda_2R^2(z)+cdots+lambda_pR^p(z)&=&z+lambda_2z^2p)^{p+1}&&+A_{2p+1}(z+cdots)^{2p+1}+cdots.array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="569" HEIGHT="76" BORDER="0"
 SRC="|."$dir".q|img691.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
R(z) + \lambda_2R^2(z) + \cdots + \lambda...
...1} \\\\
&amp; &amp; + A_{2p+1}(z + \cdots )^{2p+1} + \cdots.
\end{array}\end{displaymath}">|; 

$key = q/displaystyleR(w^2)=(w^2-a^2)^{2q+1}P(w^2)hspace{0.3in}[P(a^2)neq0],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="370" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1470.png"
 ALT="$\displaystyle R(w^2) = (w^2 - a^2)^{2q+1}P(w^2) \hspace{0.3in} [P(a^2) \neq 0],$">|; 

$key = q/{displaymath}sigma_{(n-1)h}=R_h(sigma_{-nh}),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1123.png"
 ALT="\begin{displaymath}
\sigma_{(n-1)h} = R_h(\sigma_{-nh}),
\end{displaymath}">|; 

$key = q/{displaymath}R_{q-1}[R(z)]=S(z)=mbox{polinomioen}hspace{0.2cm}z.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="315" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img232.png"
 ALT="\begin{displaymath}
R_{q-1}[R(z)] = S(z) = \mbox{ polinomio en }\hspace{0.2cm} z.
\end{displaymath}">|; 

$key = q/pm1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$\pm1$">|; 

$key = q/{displaymath}a_h+A_hs^h=A_hs+a_h,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img796.png"
 ALT="\begin{displaymath}
a_h + A_hs^h = A_hs + a_h,
\end{displaymath}">|; 

$key = q/C_{-n})({C'}_{-(n-1)},{C'}_{-n});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1457.png"
 ALT="$C_{-n})({C'}_{-(n-1)}, {C'}_{-n})$">|; 

$key = q/t_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img404.png"
 ALT="$t_0$">|; 

$key = q/{displaymath}Phi'(t)=R'(z)left[frac{z+bi}{R(z)+bi}right]^2.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1058.png"
 ALT="\begin{displaymath}
\Phi'(t) = R'(z)\left[ \frac{z + bi}{R(z) + bi} \right]^2 .
\end{displaymath}">|; 

$key = q/midPhi'(t)midgeq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1068.png"
 ALT="$\mid\Phi'(t)\mid \geq 1$">|; 

$key = q/delta_{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1100.png"
 ALT="$\delta_{-1}$">|; 

$key = q/displaystylefrac{z}{z^m+2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1287.png"
 ALT="$\displaystyle\frac{z}{z^m + 2}$">|; 

$key = q/displaystylefrac{C}{A^k},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img261.png"
 ALT="$\displaystyle \frac{C}{A^k},$">|; 

$key = q/t^frac{1}{p}=z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="25" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img662.png"
 ALT="$t^\frac{1}{p} = z$">|; 

$key = q/{displaymath}(C_{-n},C_{-(n-1)})mbox{'o}({C'}_{-n},{C'}_{-(n-1)}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="295" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1432.png"
 ALT="\begin{displaymath}
(C_{-n}, C_{-(n-1)})   \mbox{\'o}   ({C'}_{-n}, {C'}_{-(n-1)}).
\end{displaymath}">|; 

$key = q/r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$r$">|; 

$key = q/s_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img961.png"
 ALT="$s_i$">|; 

$key = q/mu(delta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1130.png"
 ALT="$\mu(\delta)$">|; 

$key = q/alpha,alpha_1,alpha_2,...;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$\alpha, \alpha_1, \alpha_2, ...$">|; 

$key = q/[R_n(z)]^{frac{1}{q^n}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img368.png"
 ALT="$[R_n(z)]^{\frac{1}{q^n}}$">|; 

$key = q/{displaymath}R'(z)>K>m-1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1321.png"
 ALT="\begin{displaymath}
R'(z) &gt; K &gt; m - 1,
\end{displaymath}">|; 

$key = q/z=(-1)^frac{1}{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1294.png"
 ALT="$z = (-1)^\frac{1}{m}$">|; 

$key = q/w=pmsqrt{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1495.png"
 ALT="$w = \pm \sqrt{z}$">|; 

$key = q/midPhi'(t)mid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1057.png"
 ALT="$\mid \Phi'(t)\mid $">|; 

$key = q/v=d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1098.png"
 ALT="$v = d$">|; 

$key = q/F(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img750.png"
 ALT="$F(t)$">|; 

$key = q/displaystyleF[R(z)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img420.png"
 ALT="$\displaystyle F[R(z)]$">|; 

$key = q/(dgeq2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1376.png"
 ALT="$ (d\geq 2)$">|; 

$key = q/C_{-n}(ngeq1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1311.png"
 ALT="$C_{-n} (n \geq 1)$">|; 

$key = q/nmu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img447.png"
 ALT="$n\mu$">|; 

$key = q/a_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1400.png"
 ALT="$a_{-n}$">|; 

$key = q/{displaymath}0<s<1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img982.png"
 ALT="\begin{displaymath}
0 &lt; s &lt; 1.
\end{displaymath}">|; 

$key = q/{displaymath}x_n=x+nasum_0^{n-1}Re[psi(z_i)]hspace{0.3in}(z_n=x_n+iy_n).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img472.png"
 ALT="\begin{displaymath}
x_n = x + na \sum_0^{n-1}\Re[\psi(z_i)] \hspace{0.3in} (z_n = x_n + iy_n).
\end{displaymath}">|; 

$key = q/s=+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$s = +1$">|; 

$key = q/{displaymath}R'(z)=-left[(m-1)-frac{2}{z^m}right]R^2(z)z^{m-2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="309" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1310.png"
 ALT="\begin{displaymath}
R'(z) = -\left[ (m - 1) - \frac{2}{z^m} \right]R^2(z)z^{m-2}.
\end{displaymath}">|; 

$key = q/a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="$a$">|; 

$key = q/displaystyleX=x+h-sumfrac{A}{(x-a)^2+y^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1234.png"
 ALT="$\displaystyle X = x + h - \sum\frac{A}{(x - a)^2 + y^2}$">|; 

$key = q/{displaymath}R(z)=z-sumfrac{A}{z-a}hspace{0.3in}(A>0),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="271" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1258.png"
 ALT="\begin{displaymath}
R(z) = z - \sum\frac{A}{z-a} \hspace{0.3in}(A &gt; 0),
\end{displaymath}">|; 

$key = q/displaystylefrac{r}{k};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img866.png"
 ALT="$\displaystyle\frac{r}{k}$">|; 

$key = q/{displaymath}z=f(z)hspace{0.2in}(0leqtleq1){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1460.png"
 ALT="\begin{displaymath}
z = f(z) \hspace{0.2in} (0 \leq t \leq 1)
\end{displaymath}">|; 

$key = q/z_{lambdapq};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img835.png"
 ALT="$z_{\lambda pq}$">|; 

$key = q/displaystylefrac{mid1mid}{z_n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img483.png"
 ALT="$\displaystyle\frac{\mid 1\mid }{z_n}$">|; 

$key = q/midtmid=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1049.png"
 ALT="$\mid t\mid = 1$">|; 

$key = q/midz^{(p)}mid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1085.png"
 ALT="$\mid z^{(p)}\mid$">|; 

$key = q/C_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1199.png"
 ALT="$C_{-n}$">|; 

$key = q/{displaymath}{cal{D}}_{-n}({cal{D}}_{-1}<{cal{D}}_{-2}<cdots<{cal{D}}_{-n}){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1198.png"
 ALT="\begin{displaymath}
{\cal{D}}_{-n}({\cal{D}}_{-1}&lt;{\cal{D}}_{-2}&lt;\cdots &lt;{\cal{D}}_{-n})
\end{displaymath}">|; 

$key = q/{displaymath}2sum^{frac{d^2-d}{2}}_{1}frac{1}{t-1}+sum^{d+1}_{1}frac{1}{s^2-1}+1=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="264" HEIGHT="69" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="\begin{displaymath}
2\sum^{\frac{d^2 - d}{2}}_{1}\frac{1}{t - 1} + \sum^{d + 1}_{1}\frac{1}{s^2 - 1} + 1 = 0,
\end{displaymath}">|; 

$key = q/a_{-(n-1)}a_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1454.png"
 ALT="$a_{-(n-1)}a_{-n}$">|; 

$key = q/sum;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img960.png"
 ALT="$\sum$">|; 

$key = q/displaystylefrac{1}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img643.png"
 ALT="$\displaystyle\frac{1}{z}$">|; 

$key = q/R'(z)>k>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1249.png"
 ALT="$R'(z) &gt; k &gt; 1$">|; 

$key = q/R(z)=f(dt);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1348.png"
 ALT="$R(z) = f(dt)$">|; 

$key = q/displaystylefrac{(A'-A)a}{z-a^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1487.png"
 ALT="$\displaystyle\frac{(A' - A)a}{z - a^2}$">|; 

$key = q/M'B';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img467.png"
 ALT="$M'B'$">|; 

$key = q/{displaymath}z_n=na+Lambda_nn^{1-gamma}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img492.png"
 ALT="\begin{displaymath}
z_n = na + \Lambda_nn^{1-\gamma}
\end{displaymath}">|; 

$key = q/{bf{2^0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img969.png"
 ALT="$\bf 2^0$">|; 

$key = q/displaystylefrac{2pi}{pp'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img805.png"
 ALT="$\displaystyle\frac{2\pi}{pp'}$">|; 

$key = q/{calL}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img591.png"
 ALT="${\cal L}_1$">|; 

$key = q/{calD}_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1224.png"
 ALT="${\cal D}_p$">|; 

$key = q/dgeq4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1412.png"
 ALT="$d\geq 4$">|; 

$key = q/lambdamu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1220.png"
 ALT="$\lambda\mu$">|; 

$key = q/s<-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1034.png"
 ALT="$s &lt; -1$">|; 

$key = q/beta_{-n}-alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1282.png"
 ALT="$\beta_{-n} - \alpha$">|; 

$key = q/{displaymath}t_n=t+npa+ntheta'frac{pa}{2}hspace{0.3in}midtheta'midgeq1;{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img770.png"
 ALT="\begin{displaymath}
t_n = t + npa + n\theta'\frac{pa}{2} \hspace{0.3in}\mid \theta'\mid \geq 1;
\end{displaymath}">|; 

$key = q/2gammapi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img314.png"
 ALT="$2\gamma\pi$">|; 

$key = q/epsilon_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img310.png"
 ALT="$\epsilon_1$">|; 

$key = q/d=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1415.png"
 ALT="$d = 2$">|; 

$key = q/lambda_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img325.png"
 ALT="$\lambda_i$">|; 

$key = q/{displaymath}sum_{deltaslashn}P(n)=d^n+1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1127.png"
 ALT="\begin{displaymath}
\sum_{\delta/n}P(n) = d^n + 1,
\end{displaymath}">|; 

$key = q/^circ3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img348.png"
 ALT="$^\circ 3$">|; 

$key = q/A,a,k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1493.png"
 ALT="$A, a, k$">|; 

$key = q/q,q',q'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="$q, q', q''$">|; 

$key = q/{displaymath}z_n=z+na+sum_0^{n-1}psi(z_i),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img471.png"
 ALT="\begin{displaymath}
z_n = z + na + \sum_0^{n-1}\psi(z_i),
\end{displaymath}">|; 

$key = q/H(z_n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img382.png"
 ALT="$H(z_n)$">|; 

$key = q/{displaymath}lim_{n=infty}z_n=+infty.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img1218.png"
 ALT="\begin{displaymath}
\lim_{n = \infty} z_n = + \infty.
\end{displaymath}">|; 

$key = q/A,h,k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img927.png"
 ALT="$A, h, k$">|; 

$key = q/{displaymath}frac{dY}{dX}=displaystylefrac{frac{partialQ}{partialy}(A,y)}{frac{p{partialx}(A,y)}{frac{partialP}{partialx}(A,y)},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="63" BORDER="0"
 SRC="|."$dir".q|img617.png"
 ALT="\begin{displaymath}
\frac{dY}{dX} = \displaystyle\frac{\frac{\partial Q}{\partia...
...}{\partial x}(A, y)}{  \frac{\partial P}{\partial x}(A, y)},
\end{displaymath}">|; 

$key = q/{displaymath}array{{rcl}Phi^q(z)=&lim_{n=infty}left{left[R(z)_{n+1}right]^{frac{nfty}{left[R(z)_{n+1}right]}^frac{1}{q^n},array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img395.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
\Phi^q(z) = &amp; \lim_{n = \infty}\left\{\le...
...nfty}{ \left[R(z)_{n+1} \right] }^\frac{1}{q^n},
\end{array}
\end{displaymath}">|; 

$key = q/S;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img776.png"
 ALT="$\S$">|; 

$key = q/left(z=frac{1}{t},z_1=frac{1}{t_1}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img632.png"
 ALT="$\left( z = \frac{1}{t}, z_1 = \frac{1}{t_1} \right)$">|; 

$key = q/mu<a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img440.png"
 ALT="$\mu &lt; a$">|; 

$key = q/{displaymath}midR'(z)midgeqfrac{d-1}{2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1411.png"
 ALT="\begin{displaymath}
\mid R'(z)\mid \geq \frac{d-1}{2}.
\end{displaymath}">|; 

$key = q/R'(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1059.png"
 ALT="$R'(z)$">|; 

$key = q/framebox[0.75in]{{-inftyhspace{0.1in}-infty{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img952.png"
 ALT="\framebox[0.75in]{$-\infty \hspace{0.1in} -\infty$}">|; 

$key = q/lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="$\lambda$">|; 

$key = q/{C''}_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1212.png"
 ALT="${C''}_{-n}$">|; 

$key = q/displaystylefrac{A}{w-a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1485.png"
 ALT="$\displaystyle\frac{A}{w - a}$">|; 

$key = q/(C_{-1},{C'}_{-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1437.png"
 ALT="$(C_{-1}, {C'}_{-1})$">|; 

$key = q/ky>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img939.png"
 ALT="$ky &gt; 0$">|; 

$key = q/-{Large{frac{n-1}{2n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="$-\Large\frac{n-1}{2n}$">|; 

$key = q/e^{2ipifrac{m}{p}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="23" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img830.png"
 ALT="$e^{2i\pi\frac{m}{p}}$">|; 

$key = q/{displaymath}S(a_{-n})=a_{-(n-1)},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="\begin{displaymath}
S(a_{-n}) = a_{-(n-1)},
\end{displaymath}">|; 

$key = q/bar{beta};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1036.png"
 ALT="$\bar{\beta}$">|; 

$key = q/(0,1,2,dots,d-1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1392.png"
 ALT="$(0, 1,2, \dots, d-1)$">|; 

$key = q/{displaymath}t_1=S(t){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img655.png"
 ALT="\begin{displaymath}
t_1 = S(t)
\end{displaymath}">|; 

$key = q/R'(z)>k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1173.png"
 ALT="$R'(z) &gt; k$">|; 

$key = q/d-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img307.png"
 ALT="$d - 1$">|; 

$key = q/{displaymath}z_n=an+frac{b}{a}{calL}n+F(z)+varepsilon_n(z)hspace{0.3in}(limvarepsilon_n=0).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="386" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img512.png"
 ALT="\begin{displaymath}
z_n = an + \frac{b}{a}{\cal L}n + F(z) + \varepsilon_n(z) \hspace{0.3in} (\lim \varepsilon_n = 0).
\end{displaymath}">|; 

$key = q/displaystyle=z_n^{frac{1}{q^n}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img371.png"
 ALT="$\displaystyle = z_n^{\frac{1}{q^n}},$">|; 

$key = q/n^o;1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img402.png"
 ALT="$n^o \; 1$">|; 

$key = q/{displaymath}t_n=S_n(t){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img713.png"
 ALT="\begin{displaymath}
t_n = S_n(t)
\end{displaymath}">|; 

$key = q/displaystylefrac{A}{(z-overline{omega})^h}+rho,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img252.png"
 ALT="$\displaystyle \frac{A}{(z-\overline{\omega})^h} + \rho,$">|; 

$key = q/k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$k$">|; 

$key = q/Z+na;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img621.png"
 ALT="$Z + na$">|; 

$key = q/P';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img223.png"
 ALT="$P'$">|; 

$key = q/textstylevdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$\textstyle \vdots$">|; 

$key = q/{displaymath}R(z)=z+a+frac{b}{z}+frac{c}{z^p}+frac{d}{z^q}+cdots,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="282" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img562.png"
 ALT="\begin{displaymath}
R(z) = z + a + \frac{b}{z} + \frac{c}{z^p} + \frac{d}{z^q} + \cdots,
\end{displaymath}">|; 

$key = q/midpsi(z)mid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img457.png"
 ALT="$\mid \psi(z)\mid $">|; 

$key = q/midz_{n+1}mid<midz_nmid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1263.png"
 ALT="$\mid z_{n+1}\mid &lt; \mid z_n\mid$">|; 

$key = q/varepsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img290.png"
 ALT="$\varepsilon$">|; 

$key = q/{displaymath}z_1=z+a+frac{b}{z}+cdotshspace{0.3in}(aneq0).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="266" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img432.png"
 ALT="\begin{displaymath}
z_1 = z + a + \frac{b}{z} + \cdots \hspace{0.3in}(a\neq0).
\end{displaymath}">|; 

$key = q/R_p(alpha)=alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$R_p(\alpha) = \alpha$">|; 

$key = q/m-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1302.png"
 ALT="$m-1$">|; 

$key = q/R'(alpha')<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img976.png"
 ALT="$R'(\alpha') &lt; 1$">|; 

$key = q/rho+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img461.png"
 ALT="$\rho+$">|; 

$key = q/midtmid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="$\mid t \mid$">|; 

$key = q/(rho,krho);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img873.png"
 ALT="$(\rho, k\rho)$">|; 

$key = q/x_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1243.png"
 ALT="$x_0$">|; 

$key = q/(a_d,+infty);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img977.png"
 ALT="$(a_d, +\infty)$">|; 

$key = q/{displaymath}z_1=frac{z}{s}+k+frac{l}{z}+cdots{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="\begin{displaymath}
z_1 = \frac{z}{s} + k + \frac{l}{z} + \cdots
\end{displaymath}">|; 

$key = q/{displaymath}frac{Theta_0}{2pi}=0,hspace{0.3in}(alpha)0(beta)00(gamma)000(delta)0000(varepsilon),dots,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1155.png"
 ALT="\begin{displaymath}
\frac{\Theta_0}{2\pi} = 0, \hspace{0.3in}(\alpha)0(\beta)00(\gamma)000(\delta)0000(\varepsilon), \dots,
\end{displaymath}">|; 

$key = q/{displaymath}left(frac{alpha_1}{d}+frac{alpha_2}{d^2}+cdots+frac{alpha_n}{d^n}right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1419.png"
 ALT="\begin{displaymath}
\left( \frac{\alpha_1}{d} + \frac{\alpha_2}{d^2} + \cdots + \frac{\alpha_n}{d^n} \right)
\end{displaymath}">|; 

$key = q/C_{-2}^{(7)},C_{-2}^{(8)},C_{-2}^{(9)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1193.png"
 ALT="$C_{-2}^{(7)}, C_{-2}^{(8)}, C_{-2}^{(9)}$">|; 

$key = q/H(w);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1472.png"
 ALT="$H(w)$">|; 

$key = q/displaystyleReleft(frac{1}{-s'-1}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$\displaystyle \Re\left(\frac{1}{-s' - 1}\right)$">|; 

$key = q/mid{z_n}mid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img389.png"
 ALT="$\mid {z_n}\mid $">|; 

$key = q/D,D_1,D_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img346.png"
 ALT="$D, D_1, D_2$">|; 

$key = q/(z,z_1,dots.z_{n-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img913.png"
 ALT="$(z, z_1, \dots. z_{n-1})$">|; 

$key = q/{displaymath}z_n=R_n(z),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="\begin{displaymath}
z_n = R_n(z),
\end{displaymath}">|; 

$key = q/t_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img657.png"
 ALT="$t_1$">|; 

$key = q/(C_{-1},{C'}_{-n});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1416.png"
 ALT="$(C_{-1}, {C'}_{-n})$">|; 

$key = q/{displaymath}mid{H(z_n)-1}mid<Amid{z_n}midhspace{0.25in}(A,mbox{constantepositiva}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="414" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img384.png"
 ALT="\begin{displaymath}
\mid {H(z_n) - 1}\mid &lt; A\mid {z_n}\mid \hspace{0.25in}(A, \mbox{ constante positiva}).
\end{displaymath}">|; 

$key = q/2zpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1096.png"
 ALT="$2z\pi$">|; 

$key = q/z^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1334.png"
 ALT="$z^3$">|; 

$key = q/MB;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img466.png"
 ALT="$MB$">|; 

$key = q/{calA}_p+{calD}_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1223.png"
 ALT="${\cal A}_p + {\cal D}_p$">|; 

$key = q/{displaymath}sumA=-1{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="\begin{displaymath}
\sum A = -1
\end{displaymath}">|; 

$key = q/midsmidgeq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img864.png"
 ALT="$\mid s\mid \geq 1$">|; 

$key = q/{displaymath}w_1=w+A_{p+1}w^{p+1}+A_{p+2}w^{p+2}+cdots,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img688.png"
 ALT="\begin{displaymath}
w_1 = w + A_{p+1}w^{p+1} +A_{p+2}w^{p+2} + \cdots,
\end{displaymath}">|; 

$key = q/Phi^{(2)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1039.png"
 ALT="$\Phi^{(2)}$">|; 

$key = q/displaystylefrac{B}{n+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img485.png"
 ALT="$\displaystyle\frac{B}{n+1}$">|; 

$key = q/D';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img635.png"
 ALT="$D'$">|; 

$key = q/b';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img293.png"
 ALT="$b'$">|; 

$key = q/{displaymath}lambda(z)=kz+h-sumfrac{A}{z-a}hspace{0.3in}(k,A,>0){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1065.png"
 ALT="\begin{displaymath}
\lambda(z) = kz + h - \sum\frac{A}{z - a} \hspace{0.3in} (k, A, &gt; 0)
\end{displaymath}">|; 

$key = q/(alpha),(beta),(gamma),cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1156.png"
 ALT="$(\alpha),(\beta),(\gamma),\cdots$">|; 

$key = q/w-lambda_2w^2+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img727.png"
 ALT="$w - \lambda_2w^2 + \cdots$">|; 

$key = q/midxmid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1168.png"
 ALT="$\mid x\mid$">|; 

$key = q/t_1=Q(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img828.png"
 ALT="$t_1 = Q(t)$">|; 

$key = q/Re[beta_n(s)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="$\Re[\beta_n(s)]$">|; 

$key = q/+infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img599.png"
 ALT="$+\infty$">|; 

$key = q/R^{D}_{-1}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img297.png"
 ALT="$R^{D}_{-1}(z)$">|; 

$key = q/{displaymath}dsigma_{-(n-1)}=dsigma_{-n}midR'(z)midhspace{0.2in}(zmbox{sobre}C_{-n}),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1202.png"
 ALT="\begin{displaymath}
d\sigma_{-(n-1)} = d\sigma_{-n}\mid R'(z)\mid \hspace{0.2in} (z \mbox{ sobre } C_{-n}),
\end{displaymath}">|; 

$key = q/[zmidR_p(z)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img347.png"
 ALT="$[ z \mid R_p(z)]$">|; 

$key = q/e^{ialpha};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img837.png"
 ALT="$e^{i\alpha}$">|; 

$key = q/-mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img475.png"
 ALT="$-\mu$">|; 

$key = q/{calE};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img602.png"
 ALT="${\cal E}$">|; 

$key = q/framebox[0.75in]{{f(z)cdots{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img949.png"
 ALT="\framebox[0.75in]{$f(z) \cdots$}">|; 

$key = q/{displaymath}array{{rcl}z_n&=&an+frac{b}{a}{calL}n+u_n,z_{n+1}&=&an+a+frac{b}{a}{calL}(n+1)+u_{n+1}.array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="304" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img499.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
z_n &amp; = &amp; an + \frac{b}{a}{\cal L}n + u_n...
... &amp; = &amp; an + a + \frac{b}{a}{\cal L}(n+1) + u_{n+1}.
\end{array}\end{displaymath}">|; 

$key = q/b;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img292.png"
 ALT="$b$">|; 

$key = q/textstyleZ=cosPhi=cos(mvarphi+a).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1517.png"
 ALT="$\textstyle Z = \cos\Phi = \cos(m\varphi + a).$">|; 

$key = q/x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img283.png"
 ALT="$x$">|; 

$key = q/{displaymath}z_{-1}=R_{-1}(z)=alpha+frac{1}{s}(z-alpha)+()(z-alpha)^2+cdots.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="398" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img856.png"
 ALT="\begin{displaymath}
z_{-1} = R_{-1}(z) = \alpha + \frac{1}{s}(z - \alpha) + ()(z - \alpha)^2 + \cdots.
\end{displaymath}">|; 

$key = q/{displaymath}frac{x}{midzmid}>frac{midpsi(z)mid}{a}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img532.png"
 ALT="\begin{displaymath}
\frac{x}{\mid z\mid } &gt; \frac{\mid \psi(z)\mid }{a}.
\end{displaymath}">|; 

$key = q/delta_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1105.png"
 ALT="$\delta_{-n}$">|; 

$key = q/{displaymath}R'(z)=frac{lambda'(z)(z^2+b^2)+b^2+lambda^2(z)}{[z+lambda(z)]^2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1060.png"
 ALT="\begin{displaymath}
R'(z) =\frac{\lambda'(z)(z^2 + b^2) + b^2 + \lambda^2(z)}{[z + \lambda(z)]^2}
\end{displaymath}">|; 

$key = q/{displaymath}midsmid=mids'mid<1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img968.png"
 ALT="\begin{displaymath}
\mid s\mid  =  \mid s'\mid  &lt; 1.
\end{displaymath}">|; 

$key = q/{displaymath}varphi(z)=frac{1}{R(z)-z}=sumfrac{A}{z-alpha}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="\begin{displaymath}
\varphi(z) = \frac{1}{R(z) - z} = \sum \frac{A}{z - \alpha}.
\end{displaymath}">|; 

$key = q/{displaymath}G(z)=sum_1^inftyleft(frac{1}{z_n}-frac{1}{na}right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img527.png"
 ALT="\begin{displaymath}
G(z) = \sum_1^\infty\left( \frac{1}{z_n} - \frac{1}{na} \right)
\end{displaymath}">|; 

$key = q/z_q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img832.png"
 ALT="$z_q$">|; 

$key = q/w=pmi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1507.png"
 ALT="$w = \pm i$">|; 

$key = q/T=(i_1,k_1)(i_2,k_2)...(i_p,k_p);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img322.png"
 ALT="$T = (i_1, k_1)(i_2, k_2)...(i_p, k_p)$">|; 

$key = q/midsmid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\mid s \mid$">|; 

$key = q/(alpha_1,alpha_2,dots,alpha_{n?});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1340.png"
 ALT="$(\alpha_1, \alpha_2, \dots, \alpha_{n?})$">|; 

$key = q/{displaymath}F[R(z)]=sF(z){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img357.png"
 ALT="\begin{displaymath}
F[R(z)] = sF(z)
\end{displaymath}">|; 

$key = q/{displaymath}S(z)=R_q(z).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="\begin{displaymath}
S(z) = R_q(z).
\end{displaymath}">|; 

$key = q/z+o({calL}midzmid);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img594.png"
 ALT="$z + o({\cal L}\mid z\mid )$">|; 

$key = q/nomath_inline}oenomath_inline};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="10" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img349.png"
 ALT="\oe">|; 

$key = q/d^n-d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$d^n -d$">|; 

$key = q/{displaymath}array{{l}midz_1midgeqmidzmid^2-5geq4,midz_2midgeqmidz^2_1mid-5>8,hs1}-1)cdots>8cdot2^{2n-2}=2^{2n+1}>2^{n+2}.array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="379" HEIGHT="153" BORDER="0"
 SRC="|."$dir".q|img888.png"
 ALT="\begin{displaymath}
\begin{array}{l}
\mid z_1\mid \geq \mid z\mid ^2 - 5 \geq...
...cdots &gt; 8\cdot 2^{2n - 2} = 2^{2n + 1} &gt; 2^{n + 2}.
\end{array}\end{displaymath}">|; 

$key = q/psi(z_i);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img473.png"
 ALT="$\psi(z_i)$">|; 

$key = q/{displaymath}Z=F(z)=P(x,y)+iQ(x,y).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img605.png"
 ALT="\begin{displaymath}
Z = F(z) = P(x, y) + iQ(x, y).
\end{displaymath}">|; 

$key = q/[R'(alpha)=+1,R''(alpha)=0];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1264.png"
 ALT="$[R'(\alpha) = +1, R''(\alpha) = 0]$">|; 

$key = q/R(z)=z^2+5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img880.png"
 ALT="$R(z) = z^2 + 5$">|; 

$key = q/C_{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1181.png"
 ALT="$C_{-1}$">|; 

$key = q/infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img271.png"
 ALT="$\infty$">|; 

$key = q/{displaymath}sum^{d+1}_{1}xi=-1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="\begin{displaymath}
\sum^{d+1}_{1}\xi = -1.
\end{displaymath}">|; 

$key = q/alpha=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img881.png"
 ALT="$\alpha =$">|; 

$key = q/D_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img341.png"
 ALT="$D_i$">|; 

$key = q/{displaymath}midR'(z)mid>k'>1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1172.png"
 ALT="\begin{displaymath}
\mid R'(z)\mid &gt; k' &gt; 1,
\end{displaymath}">|; 

$key = q/t_1^frac{1}{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img658.png"
 ALT="$t_1^\frac{1}{p}$">|; 

$key = q/displaystylefrac{partialP}{partialx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img616.png"
 ALT="$\displaystyle\frac{\partial P}{\partial x}$">|; 

$key = q/j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1394.png"
 ALT="$j$">|; 

$key = q/y_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img614.png"
 ALT="$y_2$">|; 

$key = q/{displaymath}R_1(w)=kw-sumfrac{2Aw}{w^2-a^2}=wleft[k-sumfrac{2A}{w^2-a^2},right]{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="405" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1492.png"
 ALT="\begin{displaymath}
R_1(w) = kw - \sum\frac{2Aw}{w^2 - a^2} = w\left[ k - \sum\frac{2A}{w^2 - a^2}, \right]
\end{displaymath}">|; 

$key = q/textstyle[R_{n+1}(z)]^{frac{1}{q^{n+1}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img373.png"
 ALT="$\textstyle [R_{n+1}(z)]^{\frac{1}{q^{n+1}}}$">|; 

$key = q/{displaymath}Y=ky+sumfrac{Ay}{(x-a)^2+y^2}hspace{0.3in}(kgeq0,A>0),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="375" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img941.png"
 ALT="\begin{displaymath}
Y = ky + \sum\frac{Ay}{(x - a)^2 + y^2} \hspace{0.3in} (k \geq 0, A &gt; 0),
\end{displaymath}">|; 

$key = q/midR(z)mid<kmidzmid;(k<1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1300.png"
 ALT="$ \mid R(z)\mid &lt; k\mid z\mid \;(k &lt; 1)$">|; 

$key = q/z=f(z),z_1=f(t_1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img823.png"
 ALT="$z = f(z), z_1 = f(t_1)$">|; 

$key = q/w=pma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1475.png"
 ALT="$w = \pm a$">|; 

$key = q/{displaymath}u_{n+1}=zprod^{i=n}_{i=0}frac{u_{i+1}}{u_i}=zprod^{i=n}_{i=0}[H(z_i)]^{frac{1}{q^i}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img378.png"
 ALT="\begin{displaymath}
u_{n+1} = z\prod^{i=n}_{i=0}\frac{u_{i+1}}{u_i} = z\prod^{i=n}_{i=0}[H(z_i)]^{\frac{1}{q^i}}.
\end{displaymath}">|; 

$key = q/{displaymath}mid2+z^mmidgeqsqrt{5},hspace{0.3in}R(z)leqfrac{z}{sqrt{5}}leqfrac{2}{sqrt{5}}<1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="354" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1315.png"
 ALT="\begin{displaymath}
\mid 2 + z^m\mid \geq \sqrt{5}, \hspace{0.3in}R(z) \leq \frac{z}{\sqrt{5}}\leq\frac{2}{\sqrt{5}} &lt; 1,
\end{displaymath}">|; 

$key = q/midtmid>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="$\mid t \mid &gt; 1$">|; 

$key = q/{displaymath}psi(z)=frac{b}{z}+chi(z),hspace{0.3in}midchi(z)mid<frac{k}{midzmid^{1+beta}}hspace{0.3in}(k,beta>0).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="439" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img498.png"
 ALT="\begin{displaymath}
\psi(z) = \frac{b}{z} + \chi(z), \hspace{0.3in} \mid \chi(z)...
...\frac{k}{\mid z\mid ^{1+\beta}} \hspace{0.3in} (k, \beta &gt; 0).
\end{displaymath}">|; 

$key = q/apqb;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1434.png"
 ALT="$apqb$">|; 

$key = q/midzmidleq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1272.png"
 ALT="$\mid z\mid \leq 1$">|; 

$key = q/BAB';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img454.png"
 ALT="$BAB'$">|; 

$key = q/midz_nmid<midzmid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img580.png"
 ALT="$\mid z_n\mid &lt; \mid z\mid $">|; 

$key = q/R_{np}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img812.png"
 ALT="$R_{np}(z)$">|; 

$key = q/alpha,alpha_1,dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img429.png"
 ALT="$\alpha, \alpha_1, \dots$">|; 

$key = q/{displaymath}F(z)=z+o({calL}midzmid).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img557.png"
 ALT="\begin{displaymath}
F(z) = z + o({\cal L}\mid z\mid ).
\end{displaymath}">|; 

$key = q/{displaymath}array{{rcl}(p-1)alambda_2&=&a_{p+2},(p-2)alambda_3&=&a_{p+3}+2lambdsi_p(lambda_2,lambda_3,dots,lambda_{p-1}).array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="385" HEIGHT="132" BORDER="0"
 SRC="|."$dir".q|img703.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
(p - 1) a\lambda_2 &amp; = &amp; a_{p+2}, \\\\
(p ...
...\Psi_p(\lambda_2, \lambda_3, \dots,\lambda_{p-1}).
\end{array}\end{displaymath}">|; 

$key = q/z_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img381.png"
 ALT="$z_n$">|; 

$key = q/Phi^{(1)}(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1041.png"
 ALT="$\Phi^{(1)}(t)$">|; 

$key = q/R_p(z)=z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$R_p(z) = z$">|; 

$key = q/delta_h,delta_{p+h},delta_{2p+h},dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img415.png"
 ALT="$\delta_h, \delta_{p+h}, \delta_{2p+h}, \dots$">|; 

$key = q/{displaymath}array{{llllllll}sigma,&sigma_{-a_2},&sigma_{-a_5},&sigma_{-a_9},&dots,&sigma_{-a_{frac{n(n+1)}{2}-1}},&dots,array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="386" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img1144.png"
 ALT="\begin{displaymath}
\begin{array}{llllllll}
\sigma, &amp; \sigma_{-a_2}, &amp; \sigma_{-...
...dots, &amp; \sigma_{-a_{\frac{n(n+1)}{2}- 1}}, &amp; \dots,
\end{array}\end{displaymath}">|; 

$key = q/{calA}_{p'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1227.png"
 ALT="${\cal A}_{p'}$">|; 

$key = q/{displaymath}array{{rcl}(1+a_1)(1+a_2)dots(1+a_n)dots&<&e^{a_1+a_2+cdots+a_n+cdo1-a_2)dots(1-a_n)dots&>&1-(a_1+a_2+cdots),array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="448" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img576.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
(1 + a_1)(1 + a_2) \dots (1 + a_n) \dots ...
...ots (1 - a_n) \dots &amp; &gt; &amp; 1 - (a_1 + a_2 + \cdots),
\end{array}\end{displaymath}">|; 

$key = q/{displaymath}z_n=a(n-1)+frac{b}{a}{calL}(n-1)+F(z_1)+varepsilon_{n-1}(z_1).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="380" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img513.png"
 ALT="\begin{displaymath}
z_n = a(n-1) + \frac{b}{a}{\cal L}(n-1) + F(z_1) + \varepsilon_{n-1}(z_1).
\end{displaymath}">|; 

$key = q/c_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1229.png"
 ALT="$c_n$">|; 

$key = q/{displaymath}mid{H(z_n)-1}mid<frac{1}{2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img383.png"
 ALT="\begin{displaymath}
\mid {H(z_n) - 1}\mid &lt; \frac{1}{2}
\end{displaymath}">|; 

$key = q/[zmidS(z)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="$[z \mid S(z)]$">|; 

$key = q/displaystylefrac{1}{z_1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img644.png"
 ALT="$\displaystyle\frac{1}{z_1}$">|; 

$key = q/z_{-1}=R_{-1}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img298.png"
 ALT="$z_{-1} = R_{-1}(z)$">|; 

$key = q/A_{p+1}=a_{p+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img694.png"
 ALT="$A_{p+1} = a_{p+1}$">|; 

$key = q/sigma_{-2h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1120.png"
 ALT="$\sigma_{-2h}$">|; 

$key = q/aa_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1438.png"
 ALT="$aa_1$">|; 

$key = q/rho^d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1367.png"
 ALT="$\rho^d$">|; 

$key = q/(alpha_1,alpha_2,dots,alpha_{d-1},A);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1010.png"
 ALT="$(\alpha_1, \alpha_2, \dots,\alpha_{d-1}, A)$">|; 

$key = q/R_{n_p}(z)<C^{n_p}mid1-amid,;;(C<1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="267" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1087.png"
 ALT="$R_{n_p}(z) &lt; C^{n_p}\mid 1 - a\mid, \;\;( C &lt; 1 )$">|; 

$key = q/R''(alpha)neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img629.png"
 ALT="$R''(\alpha) \neq 0$">|; 

$key = q/frac{1}{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1104.png"
 ALT="$\frac{1}{n}$">|; 

$key = q/G;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$G$">|; 

$key = q/R'(alpha')<1;;(alpha<alpha');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img978.png"
 ALT="$R'(\alpha')&lt;1 \;\;(\alpha &lt; \alpha')$">|; 

$key = q/z=R(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$z = R(z)$">|; 

$key = q/s'=u+iv;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="$s' = u + iv$">|; 

$key = q/{displaymath}overline{omega}-overline{omega}'=frac{P(z)-P'(z)}{P(z)P'(z)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img224.png"
 ALT="\begin{displaymath}
\overline{\omega} - \overline{\omega}' = \frac{P(z) - P'(z)}{P(z)P'(z)}.
\end{displaymath}">|; 

$key = q/alpha_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1251.png"
 ALT="$\alpha_n$">|; 

$key = q/a_{j+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img972.png"
 ALT="$a_{j+1}$">|; 

$key = q/Z=R_2(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img991.png"
 ALT="$Z = R_2(z)$">|; 

$key = q/{C''}_{-(n+1)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1210.png"
 ALT="${C''}_{-(n+1)}$">|; 

$key = q/z=sz=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img821.png"
 ALT="$z = sz =$">|; 

$key = q/{displaymath}prodleft(1-frac{C'}{midz_nmid^h}right);;;;mbox{y};;;;prodleft(1+frac{C}{midz_nmid^h},right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img573.png"
 ALT="\begin{displaymath}
\prod\left( 1 - \frac{C'}{\mid z_n\mid ^h} \right) \;\;\;\; ...
...{y} \;\;\;\;\prod\left( 1 + \frac{C}{\mid z_n\mid ^h}, \right)
\end{displaymath}">|; 

$key = q/w;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img717.png"
 ALT="$w$">|; 

$key = q/gamma_{-1},gamma_{-2},dots,gamma_{-n},dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1103.png"
 ALT="$\gamma_{-1}, \gamma_{-2}, \dots, \gamma_{-n}, \dots$">|; 

$key = q/delta,delta_p,delta_{2p},dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img413.png"
 ALT="$\delta, \delta_p, \delta_{2p}, \dots$">|; 

$key = q/displaystyleW=sqrt{R(w^2)}=(w-a)^{q+frac{1}{2}}H(w),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1471.png"
 ALT="$\displaystyle W = \sqrt{R(w^2)} = (w - a)^{q+\frac{1}{2}}H(w),$">|; 

$key = q/{displaymath}z_1-alpha=s(z-alpha)+k(z-alpha)^2+cdots{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="\begin{displaymath}
z_1 - \alpha = s(z - \alpha) + k(z - \alpha)^2 + \cdots
\end{displaymath}">|; 

$key = q/R'(alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$R' (\alpha)$">|; 

$key = q/qgeq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$q \geq 1$">|; 

$key = q/(midzmid<1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1329.png"
 ALT="$(\mid z\mid &lt; 1)$">|; 

$key = q/{displaymath}Z=R(z)=X+iY,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1162.png"
 ALT="\begin{displaymath}
Z = R(z) = X + iY,
\end{displaymath}">|; 

$key = q/sigma_{-3h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1121.png"
 ALT="$\sigma_{-3h}$">|; 

$key = q/{displaymath}z_n=frac{1}{na+frac{a^2-b}{a}{calL}n+F(z)+varepsilon_n}hspace{0.3in}(limvarepsilon_n=0),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="386" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img638.png"
 ALT="\begin{displaymath}
z_n = \frac{1}{na + \frac{a^2 - b}{a}{\cal L}n + F(z) + \varepsilon_n} \hspace{0.3in} (\lim \varepsilon_n = 0),
\end{displaymath}">|; 

$key = q/{displaymath}R_n(z)=R_{n-1}[R(z)]=c'{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img279.png"
 ALT="\begin{displaymath}
R_n(z) = R_{n-1}[R(z)] = c'
\end{displaymath}">|; 

$key = q/(K'<K);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1352.png"
 ALT="$(K' &lt; K)$">|; 

$key = q/displaystylefrac{2pi}{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img652.png"
 ALT="$\displaystyle\frac{2\pi}{p}$">|; 

$key = q/s=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="$s = 1$">|; 

$key = q/z_1=e^{ialpha}z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img839.png"
 ALT="$z_1 = e^{i\alpha}z$">|; 

$key = q/bi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1046.png"
 ALT="$bi$">|; 

$key = q/z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$z$">|; 

$key = q/nalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img803.png"
 ALT="$n\alpha$">|; 

$key = q/displaystyleR(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img251.png"
 ALT="$\displaystyle R(z)$">|; 

$key = q/N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img401.png"
 ALT="$N$">|; 

$key = q/{displaymath}G(z)=sum_1^{infty}frac{-z}{naz_n}+sum_1^{infty}frac{-Theta_n{calL}n}{naz_n}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img542.png"
 ALT="\begin{displaymath}
G(z) = \sum_1^{\infty}\frac{-z}{naz_n} + \sum_1^{\infty}\frac{- \Theta_n {\cal L}n}{naz_n}.
\end{displaymath}">|; 

$key = q/=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1383.png"
 ALT="$ = 0$">|; 

$key = q/Z=F(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img600.png"
 ALT="$Z = F(z)$">|; 

$key = q/{displaymath}sumfrac{t}{s-1}+sumprime[a_{-t}+1]=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="\begin{displaymath}
\sum\frac{t}{s-1} + \sum\prime[a_{-t} + 1] = 0
\end{displaymath}">|; 

$key = q/framebox[3.95in]{{-inftyhspace{0.5in}a_1hspace{0.6in}a_2hspace{0.2in}cdotshspace{0.2in}a_{d-1}hspace{0.6in}a_dhspace{0.4in}+infty{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img948.png"
 ALT="\framebox[3.95in]{$-\infty \hspace{0.5in} a_1 \hspace{0.6in} a_2 \hspace{0.2in} \cdots \hspace{0.2in} a_{d-1} \hspace{0.6in} a_d \hspace{0.4in} +\infty$}">|; 

$key = q/displaystylex.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img282.png"
 ALT="$\displaystyle x.$">|; 

$key = q/{displaymath}dsigma_{-(n-1)}=midR'(z)middsigma_{-n},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1108.png"
 ALT="\begin{displaymath}
d\sigma_{-(n-1)} = \mid R'(z)\mid d\sigma_{-n},
\end{displaymath}">|; 

$key = q/{displaymath}z_{-n}={displaystylerho}^{textstylefrac{1}{d^n}}{displaystyle{e}}^{ac{2iNpi}{d^n}}hspace{0.3in}(mbox{para}z=rho>0).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="302" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img1408.png"
 ALT="\begin{displaymath}
z_{-n} = {\displaystyle\rho}^{\textstyle\frac{1}{d^n}}{\disp...
...\frac{2iN\pi}{d^n}} \hspace{0.3in} (\mbox{para }z = \rho &gt; 0).
\end{displaymath}">|; 

$key = q/L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img295.png"
 ALT="$L$">|; 

$key = q/muslasha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img449.png"
 ALT="$\mu / a$">|; 

$key = q/R_{q-1}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img235.png"
 ALT="$R_{q-1}(z)$">|; 

$key = q/displaystyleR_{n-1}(x);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img280.png"
 ALT="$\displaystyle R_{n-1}(x)$">|; 

$key = q/F'(alpha)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img359.png"
 ALT="$F'(\alpha) = 1$">|; 

$key = q/R(z)=z^2-frac{5}{4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img890.png"
 ALT="$R(z) = z^2 - \frac{5}{4}$">|; 

$key = q/+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$+1$">|; 

$key = q/cosvarphi=z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1521.png"
 ALT="$\cos\varphi = z$">|; 

$key = q/R_n(z,lambda);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="$R_n(z, \lambda)$">|; 

$key = q/{Large{frac{1}{midzmid};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img575.png"
 ALT="$\Large\frac{1}{\mid z\mid }$">|; 

$key = q/(x<0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img760.png"
 ALT="$(x &lt; 0)$">|; 

$key = q/{displaymath}c'=R_{n-1}(c).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img284.png"
 ALT="\begin{displaymath}
c' = R_{n-1}(c).
\end{displaymath}">|; 

$key = q/cosvarphi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1519.png"
 ALT="$\cos\varphi$">|; 

$key = q/textstyleW=tanfrac{Phi}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1515.png"
 ALT="$\textstyle W = \tan\frac{\Phi}{2},$">|; 

$key = q/displaystylefrac{C}{a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img536.png"
 ALT="$\displaystyle\frac{C}{a}$">|; 

$key = q/sigma_{-a_2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1138.png"
 ALT="$\sigma_{-a_2}$">|; 

$key = q/gamma_{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1102.png"
 ALT="$\gamma_{-2}$">|; 

$key = q/delta_1,delta_{p+1},delta_{2p+1}dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img414.png"
 ALT="$\delta_1, \delta_{p+1}, \delta_{2p+1}\dots$">|; 

$key = q/midTheta_nmid<Theta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img543.png"
 ALT="$\mid \Theta_n\mid &lt; \Theta$">|; 

$key = q/qpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img924.png"
 ALT="$q\pi$">|; 

$key = q/2p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img678.png"
 ALT="$2p$">|; 

$key = q/{displaymath}array{{rcl}midz_nmid&>&Knmidz_n-amid&<&K'{calL}n;array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img505.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
\mid z_n\mid &amp; &gt; &amp; Kn \\\\
\mid z_n - a\mid &amp; &lt; &amp; K'{\cal L}n;
\end{array}\end{displaymath}">|; 

$key = q/{displaymath}R'(z)=1-frac{b}{z^2}-frac{pc}{z^{p+1}}-cdots{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img564.png"
 ALT="\begin{displaymath}
R'(z) = 1 - \frac{b}{z^2} - \frac{pc}{z^{p+1}} - \cdots
\end{displaymath}">|; 

$key = q/R^{(1)}(z)=lambda(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1054.png"
 ALT="$R^{(1)}(z) = \lambda(z)$">|; 

$key = q/displaystyle0hspace{0.1in}(Lgeq0),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$\displaystyle 0 \hspace{0.1in} (L \geq 0),$">|; 

$key = q/alpha,alpha_1,dots,alpha_{p-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img419.png"
 ALT="$\alpha, \alpha_1, \dots, \alpha_{p-1}$">|; 

$key = q/{displaymath}2h+sumfrac{A}{sqrt{z}+a}-sumfrac{A}{sqrt{z}-a}=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1483.png"
 ALT="\begin{displaymath}
2h + \sum\frac{A}{\sqrt{z} + a} - \sum\frac{A}{\sqrt{z} - a} = 0
\end{displaymath}">|; 

$key = q/f(1)=f(0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1428.png"
 ALT="$f(1) = f(0)$">|; 

$key = q/midzmid=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1078.png"
 ALT="$\mid z\mid = 1$">|; 

$key = q/n>n';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1112.png"
 ALT="$n &gt; n'$">|; 

$key = q/s^p=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img800.png"
 ALT="$s^p = 1$">|; 

$key = q/xgeqx_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1242.png"
 ALT="$x \geq x_0$">|; 

$key = q/u_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img319.png"
 ALT="$u_k$">|; 

$key = q/{displaymath}a_{-n}a_{-(n-1)}b_{-(n-1)}b_{-n},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1446.png"
 ALT="\begin{displaymath}
a_{-n}a_{-(n-1)}b_{-(n-1)}b_{-n},
\end{displaymath}">|; 

$key = q/R'(z)-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img566.png"
 ALT="$R'(z) - 1$">|; 

$key = q/displaystylefrac{2}{3^3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1331.png"
 ALT="$\displaystyle\frac{2}{3^3}$">|; 

$key = q/{displaymath}array{{c}f(z)=Fleft[frac{1}{P^p(z)}right],f[R(z)]=f(z)+pa.array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="59" BORDER="0"
 SRC="|."$dir".q|img733.png"
 ALT="\begin{displaymath}
\begin{array}{c}
f(z) = F\left[ \frac{1}{P^p(z)} \right], \\\\
f[R(z)] = f(z) + pa.
\end{array}\end{displaymath}">|; 

$key = q/{C'}_{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1393.png"
 ALT="${C'}_{-1}$">|; 

$key = q/1+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1070.png"
 ALT="$1 + $">|; 

$key = q/{displaymath}frac{1}{s-1}+frac{1}{s'-1}+sum_1^{d-1}frac{1}{s_i-1}+1=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img999.png"
 ALT="\begin{displaymath}
\frac{1}{s -1} + \frac{1}{s' -1} + \sum_1^{d-1}\frac{1}{s_i - 1} + 1 = 0,
\end{displaymath}">|; 

$key = q/a_{-3}a_{-2}b_{-2}b_{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1445.png"
 ALT="$a_{-3}a_{-2}b_{-2}b_{-3}$">|; 

$key = q/{displaymath}array{{rcl}&Phi[R(z)]hspace{1.0cm}=hspace{1.0cm}lim_{n=infty}{left[R(z)_{n+1}right]}^frac{1}{q^n},&array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="337" HEIGHT="37" BORDER="0"
 SRC="|."$dir".q|img394.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
&amp; \Phi[R(z)] \hspace{1.0cm} = \hspace{1.0...
...}{\left [R(z)_{n+1} \right]}^\frac{1}{q^n}, &amp;
\end{array} \\\\
\end{displaymath}">|; 

$key = q/{displaymath}-frac{b(z_n-na)}{naz_n},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img504.png"
 ALT="\begin{displaymath}
-\frac{b(z_n - na)}{naz_n},
\end{displaymath}">|; 

$key = q/s=e^{ialpha}=e^{2ipifrac{m}{p}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="23" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img784.png"
 ALT="$s = e^{i\alpha} = e^{2i\pi\frac{m}{p}}$">|; 

$key = q/R^{(2)}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1043.png"
 ALT="$R^{(2)}(z)$">|; 

$key = q/P(n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1126.png"
 ALT="$P(n)$">|; 

$key = q/Delta_{(i)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img756.png"
 ALT="$\Delta_{(i)}$">|; 

$key = q/z^{kh-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img258.png"
 ALT="$z^{kh - 1}$">|; 

$key = q/frac{d^2-d}{2}geq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="44" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$\frac{d^2 - d}{2} \geq 1$">|; 

$key = q/frac{1}{q^n}log,[H(z_n)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img380.png"
 ALT="$\frac{1}{q^n}\log [H(z_n)]$">|; 

$key = q/{displaymath}lambda'(z)=k+sumfrac{A}{(z-a)^2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1066.png"
 ALT="\begin{displaymath}
\lambda'(z) = k + \sum\frac{A}{(z - a)^2}
\end{displaymath}">|; 

$key = q/s_i-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1029.png"
 ALT="$s_i - 1$">|; 

$key = q/beta=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img883.png"
 ALT="$\beta =$">|; 

$key = q/S(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img648.png"
 ALT="$S(t)$">|; 

$key = q/{displaymath}l_{-n}<frac{l_0}{{k'}^n},hspace{0.3in}lim_{n=infty}l_{-n}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1205.png"
 ALT="\begin{displaymath}
l_{-n} &lt; \frac{l_0}{{k'}^n}, \hspace{0.3in} \lim_{n = \infty}l_{-n} = 0.
\end{displaymath}">|; 

$key = q/{displaymath}G(z)=sum_1^inftyfrac{na-z_n}{naz_n}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img538.png"
 ALT="\begin{displaymath}
G(z) = \sum_1^\infty\frac{na-z_n}{naz_n}.
\end{displaymath}">|; 

$key = q/O';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1459.png"
 ALT="$O'$">|; 

$key = q/n';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$n'$">|; 

$key = q/z^p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img692.png"
 ALT="$z^p$">|; 

$key = q/gamma_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1111.png"
 ALT="$\gamma_{-n}$">|; 

$key = q/{displaymath}frac{1}{midzmid^h}+frac{1}{midz_1mid^h}+cdots+frac{1}{midz_nmid^h}+cdots{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img574.png"
 ALT="\begin{displaymath}
\frac{1}{\mid z\mid ^h} + \frac{1}{\mid z_1\mid ^h} + \cdots + \frac{1}{\mid z_n\mid ^h} + \cdots
\end{displaymath}">|; 

$key = q/displaystyle-frac{A}{z-a}=-frac{A(x-a)}{(x-a)^2+y^2}+frac{Aiy}{(x-a)^2+y^2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="354" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img931.png"
 ALT="$\displaystyle -\frac{A}{z-a} = -\frac{A(x-a)}{(x-a)^2 + y^2} + \frac{Aiy}{(x-a)^2 + y^2},$">|; 

$key = q/>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img935.png"
 ALT="$ &gt; 0$">|; 

$key = q/{displaymath}frac{1}{R(z)-z}=frac{1}{s-1}frac{1}{z-alpha}+sum_1^dfrac{1}{s_i-1}frac{1}{z-alpha_i},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="350" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1018.png"
 ALT="\begin{displaymath}
\frac{1}{R(z) - z} = \frac{1}{s - 1}\frac{1}{z - \alpha} + \sum_1^d\frac{1}{s_i - 1}\frac{1}{z - \alpha_i},
\end{displaymath}">|; 

$key = q/R_{-1}^{(alpha_1)}left[R_{-1}^{(alpha_2)}left[R_{-1}^{(alpha_3)}left[dotszright]right]right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1341.png"
 ALT="$R_{-1}^{(\alpha_1)}\left[R_{-1}^{(\alpha_2)}\left[R_{-1}^{(\alpha_3)}\left[ \dots z\right]\right]\right]$">|; 

$key = q/k=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img942.png"
 ALT="$k = 0$">|; 

$key = q/z+a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img441.png"
 ALT="$z+a$">|; 

$key = q/b,lambda_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img746.png"
 ALT="$b, \lambda_i$">|; 

$key = q/{displaymath}R(z)=alpha+s(z-alpha)+a(z-alpha)^q+cdotshspace{0.25in}(aneq0).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="407" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="\begin{displaymath}
R(z) = \alpha + s(z - \alpha) + a(z - \alpha)^q + \cdots \hspace{0.25in}(a \neq 0).
\end{displaymath}">|; 

$key = q/frac{2pi}{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img663.png"
 ALT="$\frac{2\pi}{p}$">|; 

$key = q/{displaymath}R(z)=frac{A}{(z-overline{omega})^h}+rho.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img244.png"
 ALT="\begin{displaymath}
R(z) = \frac{A}{(z-\overline{\omega})^h} + \rho.
\end{displaymath}">|; 

$key = q/displaystylefrac{3pi}{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img654.png"
 ALT="$\displaystyle\frac{3\pi}{p}$">|; 

$key = q/displaystyleksqrt{z}+h-sumfrac{A}{sqrt{z}-a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1481.png"
 ALT="$\displaystyle k\sqrt{z} + h - \sum\frac{A}{\sqrt{z} - a}$">|; 

$key = q/Theta_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1151.png"
 ALT="$\Theta_0$">|; 

$key = q/{displaymath}u_{n+1}-u_n=frac{b}{a}left[frac{1}{n}-{calL}left(1+frac{1}{n}right)]+bleft(frac{1}{z_n}-frac{1}{an}right)+chi(z_n).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="462" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img502.png"
 ALT="\begin{displaymath}
u_{n+1} - u_n = \frac{b}{a}\left[ \frac{1}{n} - {\cal L}\lef...
...ght] + b\left(\frac{1}{z_n} - \frac{1}{an}\right) + \chi(z_n).
\end{displaymath}">|; 

$key = q/n=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img287.png"
 ALT="$n=1$">|; 

$key = q/p';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img806.png"
 ALT="$p'$">|; 

$key = q/sum_1^nfrac{1}{i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img526.png"
 ALT="$\sum_1^n\frac{1}{i}$">|; 

$key = q/midcmid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1305.png"
 ALT="$\mid c \mid $">|; 

$key = q/(gamma,Gamma);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1099.png"
 ALT="$(\gamma, \Gamma)$">|; 

$key = q/displaystylefrac{z+z^d}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1375.png"
 ALT="$ \displaystyle\frac{z + z^d}{2}$">|; 

$key = q/{Large{frac{1}{R(z)-z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\Large\frac{1}{R(z)-z}$">|; 

$key = q/W=sqrt{R(w^2)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1466.png"
 ALT="$W = \sqrt{R(w^2)}$">|; 

$key = q/{displaymath}F[R(z)]=F(z)+a,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img625.png"
 ALT="\begin{displaymath}
F[R(z)] = F(z) + a,
\end{displaymath}">|; 

$key = q/pmcosmpi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1520.png"
 ALT="$\pm \cos m\pi$">|; 

$key = q/midzmid=rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1076.png"
 ALT="$\mid z\mid = \rho$">|; 

$key = q/midsmid<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$\mid s \mid &lt; 1$">|; 

$key = q/displaystyle=[R^{frac{1}{q}}(z_n)]^{frac{1}{q^n}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img374.png"
 ALT="$\displaystyle = [R^{\frac{1}{q}}(z_n)]^{\frac{1}{q^n}},$">|; 

$key = q/{displaymath}midR'(z)mid>k>1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1337.png"
 ALT="\begin{displaymath}
\mid R'(z)\mid &gt; k &gt; 1,
\end{displaymath}">|; 

$key = q/displaystylefrac{dy}{dx};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img620.png"
 ALT="$\displaystyle\frac{dy}{dx}$">|; 

$key = q/{displaymath}left{array{{lr}midXmid>k'midxmid&(k>1,k'>1),midYmid>kmidymidarray{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="76" BORDER="0"
 SRC="|."$dir".q|img1175.png"
 ALT="\begin{displaymath}
\left\{
\begin{array}{lr}
\mid X\mid &gt; k'\mid x\mid \\\\
&amp; (k &gt; 1, k' &gt; 1), \\\\
\mid Y\mid &gt; k\mid y\mid
\end{array}\right.
\end{displaymath}">|; 

$key = q/displaystyle-ksqrt{z}+h+sumfrac{A}{sqrt{z}-a};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1482.png"
 ALT="$\displaystyle -k\sqrt{z} + h + \sum\frac{A}{\sqrt{z} - a}$">|; 

$key = q/{displaymath}array{{ccccccc}(1,0)(1,1),dots,(1,d-1),(2,0),dots,(d-1,d-1),array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="402" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1399.png"
 ALT="\begin{displaymath}
\begin{array}{ccccccc}
(1,0) (1,1), \dots, (1, d-1), (2,0), \dots, (d-1, d-1),
\end{array}\end{displaymath}">|; 

$key = q/{displaymath}z=R(z)=h-sumfrac{A}{z-a}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img945.png"
 ALT="\begin{displaymath}
z = R(z) = h - \sum\frac{A}{z-a}
\end{displaymath}">|; 

$key = q/x=A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img603.png"
 ALT="$x = A$">|; 

$key = q/{displaymath}t_1=S(t),hspace{0.2in}t_2=S(t_1),hspace{0.2in}cdots,hspace{0.2in}t_n=S(t_{n-1}),hspace{0.2in}cdots{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="428" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img666.png"
 ALT="\begin{displaymath}
t_1 = S(t), \hspace{0.2in} t_2 = S(t_1), \hspace{0.2in} \cdots, \hspace{0.2in} t_n = S(t_{n-1}), \hspace{0.2in} \cdots
\end{displaymath}">|; 

$key = q/[zmidR_q(z)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img831.png"
 ALT="$[z \mid R_q(z)]$">|; 

$key = q/B'T';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img453.png"
 ALT="$B'T'$">|; 

$key = q/displaystylefrac{1}{z-A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1009.png"
 ALT="$\displaystyle\frac{1}{z - A}$">|; 

$key = q/R^{(D)}_{-1}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img291.png"
 ALT="$R^{(D)}_{-1}(z)$">|; 

$key = q/alpha=-;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1278.png"
 ALT="$\alpha = -$">|; 

$key = q/{displaymath}midXmid>k'midxmidhspace{0.3in}(k'>1){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1167.png"
 ALT="\begin{displaymath}
\mid X\mid &gt; k'\mid x\mid \hspace{0.3in}(k' &gt; 1)
\end{displaymath}">|; 

$key = q/{displaymath}sum^{frac{d^n-d}{n}}_{1}Releft(frac{1}{t-1}right)+sum^{d+1}_{1}Re[beta_n(s)]+1-frac{1}{n}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="345" HEIGHT="67" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="\begin{displaymath}
\sum^{\frac{d^n - d}{n}}_{1}\Re\left(\frac{1}{t - 1}\right) + \sum^{d + 1}_{1}\Re[\beta_n(s)] + 1 - \frac{1}{n} = 0.
\end{displaymath}">|; 

$key = q/D_{p-h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img339.png"
 ALT="$D_{p-h}$">|; 

$key = q/R_{-h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1119.png"
 ALT="$R_{-h}$">|; 

$key = q/{displaymath}Phi'(t)=frac{lambda'(z)(z^2+b^2)+lambda^2(z)+b^2}{[lambda(z)+bi]^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1063.png"
 ALT="\begin{displaymath}
\Phi'(t) = \frac{\lambda'(z)(z^2 + b^2) + \lambda^2(z) + b^2}{[\lambda(z) + bi]^2}.
\end{displaymath}">|; 

$key = q/{displaymath}R^{(D)}_{-(n+n')}(z)=R^{(D)}_{-n}[R^{(D)}_{-n'}(z)],{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="37" BORDER="0"
 SRC="|."$dir".q|img302.png"
 ALT="\begin{displaymath}
R^{(D)}_{-(n+n')}(z) = R^{(D)}_{ -n}[R^{(D)}_{-n'}(z)],
\end{displaymath}">|; 

$key = q/{displaymath}array{{ccc}R'(z)=left(frac{4}{z^3}-1right)R^2(z),&midzmid<sqrt{3},&midR(z)mid>1-varepsilon.array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="442" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img1336.png"
 ALT="\begin{displaymath}
\begin{array}{ccc}
R'(z) = \left( \frac{4}{z^3} - 1 \right) ...
...id &lt; \sqrt{3}, &amp; \mid R(z)\mid &gt; 1 - \varepsilon.
\end{array}\end{displaymath}">|; 

$key = q/displaystylefrac{2npi}{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img814.png"
 ALT="$\displaystyle\frac{2n\pi}{p}$">|; 

$key = q/{displaymath}array{{lll}mbox{(I)}&R(p)=p,&R(q)=q,mbox{(II)}&R(p)=p,&R(q)=p,mbox{&R(p)=q,&R(q)=q,mbox{(IV)}&R(p)=q,&R(q)=p.array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="99" BORDER="0"
 SRC="|."$dir".q|img1503.png"
 ALT="\begin{displaymath}\begin{array}{lll}
\mbox{(I) } &amp; R(p)=p, &amp; R(q)=q, \\\\
\mbox{...
... &amp; R(q)=q, \\\\
\mbox{(IV) } &amp; R(p)=q, &amp; R(q)=p. \\\\
\end{array}\end{displaymath}">|; 

$key = q/R_1(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1091.png"
 ALT="$R_1(z)$">|; 

$key = q/{displaymath}frac{partial}{partialz}[R_n(z)+lambda-z]{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="\begin{displaymath}\frac{\partial}{\partial z}[R_n(z) + \lambda - z] \end{displaymath}">|; 

$key = q/[R_n(z)]^{textstylefrac{1}{q^n}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img390.png"
 ALT="$[R_n(z)]^{\textstyle\frac{1}{q^n}}$">|; 

$key = q/R_n(y)=z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$R_n(y) = z$">|; 

$key = q/R(varepsilon);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img289.png"
 ALT="$R(\varepsilon)$">|; 

$key = q/{displaymath}mu<frac{C}{rhogamma}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img455.png"
 ALT="\begin{displaymath}
\mu &lt; \frac{C}{\rho\gamma}
\end{displaymath}">|; 

$key = q/{displaymath}midPhi'(t)mid=1+lambda'(z)frac{z^2+b^2}{lambda^2(z)+b^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1064.png"
 ALT="\begin{displaymath}
\mid \Phi'(t)\mid = 1 + \lambda'(z)\frac{z^2 + b^2}{\lambda^2(z) + b^2}.
\end{displaymath}">|; 

$key = q/l_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1277.png"
 ALT="$l_{-n}$">|; 

$key = q/{displaymath}sumfrac{1}{s-1}+1=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="\begin{displaymath}
\sum\frac{1}{s-1} + 1 = 0.
\end{displaymath}">|; 

$key = q/midtmid<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1050.png"
 ALT="$\mid t\mid &lt; 1$">|; 

$key = q/z=alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img361.png"
 ALT="$z = \alpha$">|; 

$key = q/A_{p+2}=A_{p+3}=cdots=A_{2p}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="243" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img689.png"
 ALT="$A_{p+2} = A_{p+3} = \cdots = A_{2p} = 0$">|; 

$key = q/displaystylew=tanfrac{varphi}{2},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1514.png"
 ALT="$\displaystyle w = \tan\frac{\varphi}{2},$">|; 

$key = q/T=Phi(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1037.png"
 ALT="$T = \Phi(t)$">|; 

$key = q/{displaymath}R'(k)>k>1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1161.png"
 ALT="\begin{displaymath}
R'(k) &gt; k &gt; 1.
\end{displaymath}">|; 

$key = q/R(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$R(z)$">|; 

$key = q/Q(x,y)=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img618.png"
 ALT="$Q(x, y) = $">|; 

$key = q/{displaymath}sum_1^inftyfrac{z}{naz_n}=sum_1^N+sum_{N+1}^infty,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="60" BORDER="0"
 SRC="|."$dir".q|img546.png"
 ALT="\begin{displaymath}
\sum_1^\infty\frac{z}{naz_n} = \sum_1^N + \sum_{N+1}^\infty,
\end{displaymath}">|; 

$key = q/sigma_{-a_n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1143.png"
 ALT="$\sigma_{-a_n}$">|; 

$key = q/midR(z)midgeq2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1274.png"
 ALT="$\mid R(z)\mid \geq 2$">|; 

$key = q/midz_{lambda+mu-1}-alphamidleqrho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img871.png"
 ALT="$\mid z_{\lambda + \mu - 1} - \alpha\mid \leq \rho$">|; 

$key = q/displaystyle+s^n(z-alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$\displaystyle + s^n(z-\alpha)$">|; 

$key = q/F(alpha)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img358.png"
 ALT="$F(\alpha) = 0$">|; 

$key = q/(a_1,a_2),(a_2,a_3),dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="159" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img954.png"
 ALT="$(a_1, a_2), (a_2, a_3), \dots$">|; 

$key = q/{displaymath}u^2+v^2=1,hspace{0.5in}u^2+v^2>1,hspace{0.5in}u^2+v^2<1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="415" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="\begin{displaymath}
u^2 + v^2 = 1, \hspace{0.5in} u^2 + v^2 &gt; 1, \hspace{0.5in} u^2 + v^2 &lt; 1,
\end{displaymath}">|; 

$key = q/{displaymath}z^2+z-frac{1}{4}=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img894.png"
 ALT="\begin{displaymath}
z^2 + z - \frac{1}{4} = 0,
\end{displaymath}">|; 

$key = q/{displaymath}z+n'a+nahspace{0.3in}mbox{y}hspace{0.3in}Z+(n+n')a,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="308" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img628.png"
 ALT="\begin{displaymath}
z + n'a + na \hspace{0.3in}\mbox{ y } \hspace{0.3in} Z + (n + n')a,
\end{displaymath}">|; 

$key = q/+pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img651.png"
 ALT="$+\pi$">|; 

$key = q/W(w);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1465.png"
 ALT="$W(w)$">|; 

$key = q/{displaymath}frac{A}{C^h}(z-rho)^{kh}+rho=frac{C}{A^k}(z-overline{omega})^{kh}+overline{omega}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img256.png"
 ALT="\begin{displaymath}
\frac{A}{C^h}(z - \rho)^{kh} + \rho = \frac{C}{A^k}(z - \overline{\omega})^{kh} + \overline{\omega}.
\end{displaymath}">|; 

$key = q/mu_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img747.png"
 ALT="$\mu_i$">|; 

$key = q/R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img233.png"
 ALT="$R$">|; 

$key = q/k>sqrt{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1338.png"
 ALT="$k &gt; \sqrt{d}$">|; 

$key = q/alpha<alpha'<alpha'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img970.png"
 ALT="$\alpha &lt; \alpha' &lt;\alpha''$">|; 

$key = q/c';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img278.png"
 ALT="$c'$">|; 

$key = q/{displaymath}R'_n(z)=R'(z)R'(z_1)dotsR'(z_{n-1});{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="266" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img570.png"
 ALT="\begin{displaymath}
R'_n(z) = R'(z)R'(z_1) \dots R' (z_{n-1});
\end{displaymath}">|; 

$key = q/(C_{-2},{C'}_{-2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1397.png"
 ALT="$(C_{-2}, {C'}_{-2})$">|; 

$key = q/-displaystylefrac{2}{z^m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1316.png"
 ALT="$-\displaystyle\frac{2}{z^m}$">|; 

$key = q/W;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1464.png"
 ALT="$W$">|; 

$key = q/z=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img891.png"
 ALT="$z = $">|; 

$key = q/z_1=R(z)=e^{ialpha}z+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img846.png"
 ALT="$z_1 = R(z) = e^{i\alpha}z + \cdots$">|; 

$key = q/k=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1270.png"
 ALT="$k = 2$">|; 

$key = q/z^{kh};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img257.png"
 ALT="$z^{kh}$">|; 

$key = q/s^r=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$s^r = 1$">|; 

$key = q/Phi=Phi^{(1)}Phi^{(2)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1040.png"
 ALT="$\Phi = \Phi^{(1)}\Phi^{(2)}$">|; 

$key = q/R(z)+lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="$R(z) + \lambda$">|; 

$key = q/D_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img288.png"
 ALT="$D_1$">|; 

$key = q/1,2,3,dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1344.png"
 ALT="$1, 2, 3, \dots$">|; 

$key = q/d-2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img987.png"
 ALT="$d - 2$">|; 

$key = q/D_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img904.png"
 ALT="$D_2$">|; 

$key = q/lambda_2,lambda_3,dots,lambda_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img704.png"
 ALT="$\lambda_2, \lambda_3, \dots, \ \lambda_p$">|; 

$key = q/midtmid=rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1365.png"
 ALT="$\mid t\mid = \rho$">|; 

$key = q/H_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img488.png"
 ALT="$H_n$">|; 

$key = q/R_2(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img992.png"
 ALT="$R_2(z)$">|; 

$key = q/A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="$A$">|; 

$key = q/{displaymath}z_1=z^q+az^{q+r}+cdots=R(z)hspace{0.25in}(q>1),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="324" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img367.png"
 ALT="\begin{displaymath}
z_1 = z^q + az^{q+r} + \cdots = R(z) \hspace{0.25in} (q&gt;1),
\end{displaymath}">|; 

$key = q/{displaymath}midR(z)mid<cmidzmidhspace{0.3in}(0<midcmid<1){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1079.png"
 ALT="\begin{displaymath}
\mid R(z)\mid &lt; c\mid z\mid \hspace{0.3in} (0 &lt; \mid c\mid &lt; 1)
\end{displaymath}">|; 

$key = q/h>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img584.png"
 ALT="$h &gt; 1$">|; 

$key = q/xi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\xi$">|; 

$key = q/displaystyleF_2[R(z)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img424.png"
 ALT="$\displaystyle F_2[R(z)]$">|; 

$key = q/displaystyleR_n(z)-z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$\displaystyle R_n(z) - z$">|; 

$key = q/n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$n$">|; 

$key = q/z_{n+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img500.png"
 ALT="$z_{n+1}$">|; 

$key = q/C_{-1}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1433.png"
 ALT="$C_{-1}'$">|; 

$key = q/{displaymath}U_n(z)=frac{R_n(z)-z}{R(z)-z}=z^{d^n-d}+cdots+P_n(a)=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="374" HEIGHT="52" BORDER="0"
 SRC="|."$dir".q|img909.png"
 ALT="\begin{displaymath}
U_n(z) = \frac{R_n(z) - z}{R(z) - z} = z^{d^n -d} + \cdots + P_n(a) = 0.
\end{displaymath}">|; 

$key = q/sigma_{-a_4};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1141.png"
 ALT="$\sigma_{-a_4}$">|; 

$key = q/{displaymath}R'(z)=frac{1+dz^{d-1}}{2}mbox{y}midzmidgeq1,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img1410.png"
 ALT="\begin{displaymath}
R'(z) = \frac{1 + dz^{d-1}}{2}   \mbox{y}    \mid z\mid \geq 1,
\end{displaymath}">|; 

$key = q/d=3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1189.png"
 ALT="$d=3$">|; 

$key = q/(0,1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1427.png"
 ALT="$(0, 1)$">|; 

$key = q/pq;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1502.png"
 ALT="$pq$">|; 

$key = q/{displaymath}array{{l}(z+a_{p+1}z^{p+1}+a_{p+2}z^{p+2}+cdots+a_{2p}z^{2p}+cdots)2z+cdots+lambda_pz^{p-1})^{p+1}+Hz^{2p+1}.array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="479" HEIGHT="145" BORDER="0"
 SRC="|."$dir".q|img695.png"
 ALT="\begin{displaymath}
\begin{array}{l}
(z + a_{p+1}z^{p+1} + a_{p+2}z^{p+2} + \cdo...
..._2z + \cdots + \lambda_pz^{p-1})^{p+1} + Hz^{2p+1}.
\end{array}\end{displaymath}">|; 

$key = q/{displaymath}frac{1}{z}R^{frac{1}{q}}(z)=1+lz+cdots.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img377.png"
 ALT="\begin{displaymath}
\frac{1}{z}R^{\frac{1}{q}}(z) = 1 + lz + \cdots .
\end{displaymath}">|; 

$key = q/displaystylena(z-alpha)^q+cdots,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$\displaystyle na(z - \alpha)^q + \cdots,$">|; 

$key = q/t_n^{-frac{1}{p}}=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img738.png"
 ALT="$t_n^{-\frac{1}{p}} =$">|; 

$key = q/{displaymath}R'(alpha)>1,hspace{0.3in}R''(alpha'')>1;{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img974.png"
 ALT="\begin{displaymath}
R'(\alpha) &gt; 1, \hspace{0.3in} R''(\alpha'') &gt; 1;
\end{displaymath}">|; 

$key = q/{displaymath}array{{rcl}&Phi[R(z)]hspace{1.0cm}=hspace{1.0cm}lim_{n=infty}{left[R(z){n+1}right]}^frac{1}{q^n},&array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="355" HEIGHT="37" BORDER="0"
 SRC="|."$dir".q|img392.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
&amp; \Phi[R(z)] \hspace{1.0cm} = \hspace{1.0...
...}{\left [R(z) {n+1} \right]}^\frac{1}{q^n}, &amp;
\end{array} \\\\
\end{displaymath}">|; 

$key = q/2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$2$">|; 

$key = q/displaystyleR'_p(alpha_2);;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$\displaystyle R'_p(\alpha_2) ;$">|; 

$key = q/{displaymath}array{{rcl}Phi^q(z)=&lim_{n=infty}left{left[R(z){n+1}right]^{frac{1infty}{left[R(z){n+1}right]}^frac{1}{q^n},array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="511" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img393.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
\Phi^q(z) = &amp; \lim_{n = \infty}\left\{\le...
...nfty}{ \left[R(z) {n+1} \right] }^\frac{1}{q^n},
\end{array}
\end{displaymath}">|; 

$key = q/alphabeta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1211.png"
 ALT="$\alpha\beta$">|; 

$key = q/BT;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img452.png"
 ALT="$BT$">|; 

$key = q/displaystylefrac{1}{s_i-0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1016.png"
 ALT="$\displaystyle\frac{1}{s_i - 0}$">|; 

$key = q/c=R(zeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1380.png"
 ALT="$c = R(\zeta)$">|; 

$key = q/displaystyleR(z)-z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="$\displaystyle R(z) - z$">|; 

$key = q/{displaymath}F[R_p(z)]=sF(z)hspace{0.35in}[s=R'(alpha)R'(alpha_1)dotsR'(alpha_{p-1})].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="429" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img428.png"
 ALT="\begin{displaymath}
F[R_p(z)] = sF(z) \hspace{0.35in} [s = R'(\alpha)R'(\alpha_1) \dots R'(\alpha_{p-1})].
\end{displaymath}">|; 

$key = q/R_{lambdap-q}=f_lambda(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img817.png"
 ALT="$R_{\lambda p - q} = f_\lambda(z)$">|; 

$key = q/0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img270.png"
 ALT="$0$">|; 

$key = q/2P;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1169.png"
 ALT="$2P$">|; 

$key = q/R^{(2)}(z)=z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1055.png"
 ALT="$R^{(2)}(z) = z$">|; 

$key = q/R_n(0)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img781.png"
 ALT="$R_n(0) = 0$">|; 

$key = q/{displaymath}R(b)=R(b')=a;{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img294.png"
 ALT="\begin{displaymath}
R(b) = R(b') = a ;
\end{displaymath}">|; 

$key = q/C_{-n'}(n'>n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1342.png"
 ALT="$C_{-n'}(n' &gt; n)$">|; 

$key = q/{displaymath}P(z_n)=frac{1}{sqrt[p]{npa+frac{b}{a}{calL}n+f(z)+varepsilon_n}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="284" HEIGHT="59" BORDER="0"
 SRC="|."$dir".q|img732.png"
 ALT="\begin{displaymath}
P(z_n) = \frac{1}{\sqrt[p]{npa + \frac{b}{a} {\cal L}n + f(z) + \varepsilon_n}},
\end{displaymath}">|; 

$key = q/displaystylea(z-alpha)^q+cdots,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$\displaystyle a(z - \alpha)^q + \cdots,$">|; 

$key = q/{displaymath}xi=R_h(xi).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1124.png"
 ALT="\begin{displaymath}
\xi = R_h(\xi).
\end{displaymath}">|; 

$key = q/sigma';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1136.png"
 ALT="$\sigma'$">|; 

$key = q/{displaymath}midz_1-alphamid=midR(z)-alphamid>kmidz-alphamid.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="310" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img848.png"
 ALT="\begin{displaymath}
\mid z_1 - \alpha\mid = \mid R(z) - \alpha\mid &gt; k\mid z - \alpha\mid .
\end{displaymath}">|; 

$key = q/A>;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img537.png"
 ALT="$A &gt;$">|; 

$key = q/G(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img541.png"
 ALT="$G(z)$">|; 

$key = q/R_{-n}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$R_{-n}(z)$">|; 

$key = q/displaystylefrac{pa}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img767.png"
 ALT="$\displaystyle\frac{pa}{2}$">|; 

$key = q/E';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1116.png"
 ALT="$E'$">|; 

$key = q/{displaymath}frac{partial}{partialz}R_n(z,lambda){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="\begin{displaymath}
\frac{\partial}{\partial z}R_n(z, \lambda)\end{displaymath}">|; 

$key = q/L_1,...,L_p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img321.png"
 ALT="$L_1, ..., L_p$">|; 

$key = q/(1-a,1+a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1082.png"
 ALT="$(1-a, 1+a)$">|; 

$key = q/frac{delta}{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1128.png"
 ALT="$\frac{\delta}{n}$">|; 

$key = q/{displaymath}mbox{longitud}s_{n+1}>kmbox{longitudes}s_nhspace{0.3in}(k>1),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1255.png"
 ALT="\begin{displaymath}
\mbox{ longitud } s_{n+1} &gt; k \mbox{ longitudes }s_n \hspace{0.3in} (k &gt; 1),
\end{displaymath}">|; 

$key = q/{displaymath}F(t)=t+o[{calL}(t)].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img716.png"
 ALT="\begin{displaymath}
F(t) = t + o[{\cal L}(t)].
\end{displaymath}">|; 

$key = q/{displaymath}R(z)-overline{omega}=frac{A}{(z-overline{omega})^h}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img265.png"
 ALT="\begin{displaymath}
R(z) - \overline{\omega} = \frac{A}{(z-\overline{\omega})^h}.
\end{displaymath}">|; 

$key = q/z_1=R(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$z_1 = R(z)$">|; 

$key = q/w=t^{-frac{1}{p}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="25" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img708.png"
 ALT="$w = t^{-\frac{1}{p}}$">|; 

$key = q/left(A>frac{C}{a}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img587.png"
 ALT="$\left(A &gt; \frac{C}{a} \right)$">|; 

$key = q/F;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img754.png"
 ALT="$F$">|; 

$key = q/Phi'(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1062.png"
 ALT="$\Phi'(t)$">|; 

$key = q/R'(z)>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1248.png"
 ALT="$R'(z) &gt; 1$">|; 

$key = q/displaystylefrac{1}{alpha-z_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1355.png"
 ALT="$\displaystyle\frac{1}{\alpha - z_0}$">|; 

$key = q/P(z_n)=w_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img735.png"
 ALT="$P(z_n) = w_n$">|; 

$key = q/displaystylefrac{C}{midzmid};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img534.png"
 ALT="$\displaystyle\frac{C}{\mid z\mid }$">|; 

$key = q/cal{D};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1174.png"
 ALT="$\cal{D}$">|; 

$key = q/displaystyle+as^{n-1}[1+s^{q-1}+s^{2(q-1)}+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$\displaystyle + as^{n-1}[ 1 + s^{q-1} + s^{2(q-1)} + \cdots$">|; 

$key = q/K=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1074.png"
 ALT="$K = 0$">|; 

$key = q/z_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img921.png"
 ALT="$z_0$">|; 

$key = q/displaystylefrac{N+1}{midzmid^h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img579.png"
 ALT="$\displaystyle\frac{N + 1}{\mid z\mid ^h}$">|; 

$key = q/{displaymath}w_1=w-aw^{p+1}+A_{2p+1}w^{2p+1}+cdots=Q(w),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img707.png"
 ALT="\begin{displaymath}
w_1 = w - aw^{p+1} + A_{2p+1}w^{2p+1} + \cdots = Q(w),
\end{displaymath}">|; 

$key = q/alpha=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img630.png"
 ALT="$\alpha = 0$">|; 

$key = q/{displaymath}midG(z)mid<C'{calL}midzmid,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img555.png"
 ALT="\begin{displaymath}
\mid G(z)\mid &lt; C'{\cal L}\mid z\mid ,
\end{displaymath}">|; 

$key = q/framebox[0.75in]{{zcdots{};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img947.png"
 ALT="\framebox[0.75in]{$z \cdots$}">|; 

$key = q/Ox;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img448.png"
 ALT="$Ox$">|; 

$key = q/{displaymath}t_1=t+a+frac{a^2-b}{t}+cdots.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img633.png"
 ALT="\begin{displaymath}
t_1 = t + a + \frac{a^2 - b}{t} + \cdots.
\end{displaymath}">|; 

$key = q/{displaymath}frac{midzmid}{aK}sum_{N+1}^inftyfrac{1}{n^2}<frac{midzmid}{NaK},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="57" BORDER="0"
 SRC="|."$dir".q|img553.png"
 ALT="\begin{displaymath}
\frac{\mid z\mid }{aK}\sum_{N+1}^\infty\frac{1}{n^2} &lt; \frac{\mid z\mid }{NaK},
\end{displaymath}">|; 

$key = q/m+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1293.png"
 ALT="$m+1$">|; 

$key = q/lambda_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img328.png"
 ALT="$\lambda_2$">|; 

$key = q/d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$d$">|; 

$key = q/{displaymath}left{array{{llll}D^0&D^1&dots&D^{p'-1},D^0_1&D^1_1&dots&D^{p'-1}_1,{p-1}&D^1_{p-1}&dots&D^{p'-1}_{p-1},array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="105" BORDER="0"
 SRC="|."$dir".q|img809.png"
 ALT="\begin{displaymath}
\left\{
\begin{array}{llll}
D^0 &amp; D^1 &amp; \dots &amp; D^{p'-1}, \\\\...
...{p-1} &amp; D^1_{p-1} &amp; \dots &amp; D^{p'-1}_{p-1},
\end{array}\right.
\end{displaymath}">|; 

$key = q/alpha';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img975.png"
 ALT="$\alpha'$">|; 

$key = q/0,1,2,dots,q-2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img408.png"
 ALT="$0, 1, 2, \dots, q-2$">|; 

$key = q/d+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$d + 1$">|; 

$key = q/R_{-4}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img343.png"
 ALT="$R_{-4}(z)$">|; 

$key = q/midzmid=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1308.png"
 ALT="$\mid z \mid = 2$">|; 

$key = q/{calL};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img590.png"
 ALT="${\cal L}$">|; 

$key = q/midzmidgeq3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img887.png"
 ALT="$\mid z\mid \geq 3$">|; 

$key = q/{displaymath}2u+1+P=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img965.png"
 ALT="\begin{displaymath}
2u + 1 + P = 0.
\end{displaymath}">|; 

$key = q/{displaymath}P(n)=summu(delta)d^{mbox{{{normalsize{frac{n}{delta}{}}equiv0hspace{0.3in}(mbox{mod}n),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img1132.png"
 ALT="\begin{displaymath}
P(n) = \sum\mu(\delta)d^{\mbox{$\normalsize\frac{n}{\delta}$}} \equiv 0 \hspace{0.3in}(\mbox{mod }n),
\end{displaymath}">|; 

$key = q/j+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1395.png"
 ALT="$j + 1$">|; 

$key = q/{displaymath}h-sumfrac{Aa}{z-a^2}=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1484.png"
 ALT="\begin{displaymath}
h - \sum\frac{Aa}{z - a^2} = 0.
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{z-a_i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1007.png"
 ALT="$\displaystyle\frac{1}{z - a_i}$">|; 

$key = q/alpha_1,alpha_2,dots,alpha_{d-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img997.png"
 ALT="$ \alpha_1, \alpha_2, \dots, \alpha_{d - 1} $">|; 

$key = q/a^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1469.png"
 ALT="$a^2$">|; 

$key = q/z,R(z),R_2(z),dots,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img819.png"
 ALT="$z, R(z), R_2(z), \dots,$">|; 

$key = q/{displaymath}t=frac{z-beta}{z--{barbeta}},hspace{0.3in}T=frac{Z-beta}{Z-bar{beta}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1035.png"
 ALT="\begin{displaymath}
t = \frac{z - \beta}{z - \-{\bar\beta}}, \hspace{0.3in} T = \frac{Z - \beta}{Z - \bar{\beta}},
\end{displaymath}">|; 

$key = q/Phi^{(1)}(t)=Psi(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1052.png"
 ALT="$\Phi^{(1)}(t) = \Psi(t)$">|; 

$key = q/{displaymath}R(z)=-kz-h+sumfrac{A}{z-a},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img990.png"
 ALT="\begin{displaymath}
R(z) = - kz - h + \sum\frac{A}{z-a},
\end{displaymath}">|; 

$key = q/displaystyle+as^{n-1}[1+s^{q-1}+s^{2(q-1)}+cdots+s^{(n-1)(q-1)}](z-alpha)^q+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$\displaystyle + as^{n-1}[1 + s^{q-1} + s^{2(q-1)} + \cdots
+ s^{(n-1)(q-1)}](z - \alpha)^q + \cdots$">|; 

$key = q/gamma^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img301.png"
 ALT="$\gamma^n$">|; 

$key = q/c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img276.png"
 ALT="$c$">|; 

$key = q/(p'geq1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img836.png"
 ALT="$(p'\geq 1)$">|; 

$key = q/displaystyleF_1[R(z)];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img422.png"
 ALT="$\displaystyle F_1[R(z)]$">|; 

$key = q/p+q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="$p + q$">|; 

$key = q/0<gamma<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img489.png"
 ALT="$0 &lt; \gamma &lt; 1$">|; 

$key = q/displaystylefrac{1}{n_p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1088.png"
 ALT="$\displaystyle\frac{1}{n_p}$">|; 

$key = q/sum{airesC_{-n}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1324.png"
 ALT="$\sum{airesC_{-n}}$">|; 

$key = q/K>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1333.png"
 ALT="$K &gt; 1$">|; 

$key = q/{displaymath}frac{w-i}{w+i}=thspace{0.3in}frac{W-i}{W+i}=T,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1508.png"
 ALT="\begin{displaymath}
\frac{w-i}{w+i} = t \hspace{0.3in} \frac{W-i}{W+i} = T,
\end{displaymath}">|; 

$key = q/(x>0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img759.png"
 ALT="$(x &gt; 0)$">|; 

$key = q/displaystylefrac{{calL}n}{n^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img508.png"
 ALT="$\displaystyle\frac{{\cal L}n}{n^2}$">|; 

$key = q/mu(1)=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1131.png"
 ALT="$\mu(1) = 1$">|; 

$key = q/alpha_1<alpha<alpha_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1030.png"
 ALT="$\alpha_1 &lt; \alpha &lt; \alpha_2$">|; 

$key = q/t=+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="$t = +1$">|; 

$key = q/{displaymath}R'(z)=+1,hspace{0.3in}R''(z)=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1033.png"
 ALT="\begin{displaymath}
R'(z) = +1, \hspace{0.3in} R''(z) = 0,
\end{displaymath}">|; 

$key = q/gamma;;gamma_{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1094.png"
 ALT="$\gamma;\; \gamma_{-1}$">|; 

$key = q/{C'}_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1386.png"
 ALT="${C'}_{-n}$">|; 

$key = q/{displaymath}z_1=R(z)=z+frac{a}{z^{p-1}}+frac{b}{z^p}+cdots=zleft(1+frac{a}{z^p}+frac{b}{z^{p+1}}+cdotsright).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="495" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img645.png"
 ALT="\begin{displaymath}
z_1 = R(z) = z + \frac{a}{z^{p-1}} + \frac{b}{z^p} + \cdots = z\left( 1 + \frac{a}{z^p} + \frac{b}{z^{p+1}} + \cdots \right).
\end{displaymath}">|; 

$key = q/midF'(z)mid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img572.png"
 ALT="$\mid F'(z)\mid $">|; 

$key = q/{delta'}_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1423.png"
 ALT="${\delta'}_{-n}$">|; 

$key = q/c,R_3(c),R(c''){mboxy}R_2(c');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img344.png"
 ALT="$c, R_3(c), R(c'') {\mbox y} R_2(c')$">|; 

$key = q/displaystylefrac{C}{(z-rho)^k}+overline{omega},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img254.png"
 ALT="$\displaystyle \frac{C}{(z-\rho)^k} + \overline{\omega},$">|; 

$key = q/midz-alphamidleqrho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img853.png"
 ALT="$\mid z - \alpha\mid \leq \rho$">|; 

$key = q/(ZmidZ+na);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img622.png"
 ALT="$(Z \mid Z + na)$">|; 

$key = q/{bf{1^0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img955.png"
 ALT="$\bf 1^0$">|; 

$key = q/{displaymath}R_n(z)=z.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="\begin{displaymath}
R_n(z) = z.
\end{displaymath}">|; 

$key = q/overline{omega}=overline{omega}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img225.png"
 ALT="$\overline{\omega} = \overline{\omega}'$">|; 

$key = q/z=alpha=a+bi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1011.png"
 ALT="$z = \alpha = a + bi$">|; 

$key = q/displaystyleR_{q-1}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img253.png"
 ALT="$\displaystyle R_{q-1}(z)$">|; 

$key = q/a_{-1}abb_{-1},R_{-1}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1442.png"
 ALT="$a_{-1}abb_{-1}, R_{-1}(z)$">|; 

$key = q/(w-a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1474.png"
 ALT="$(w-a)$">|; 

$key = q/R_{q-1}(infty)=overline{omega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img231.png"
 ALT="$R_{q-1}(\infty) = \overline{\omega}$">|; 

$key = q/{displaymath}sigma,;;sigma',;;sigma,;;sigma',;;sigma'',;;sigma,;;sigma',;;sigma'',;;sigma''',;;sigma,;;sigma',;;dots.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="404" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img1135.png"
 ALT="\begin{displaymath}
\sigma, \;\; \sigma', \;\; \sigma, \;\; \sigma', \;\; \sigma...
...gma'', \;\; \sigma''', \;\; \sigma, \;\; \sigma', \;\; \dots .
\end{displaymath}">|; 

$key = q/displaystylefrac{r}{k},frac{r}{k^2},cdots,frac{r}{k^n},cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img879.png"
 ALT="$\displaystyle\frac{r}{k}, \frac{r}{k^2}, \cdots, \frac{r}{k^n}, \cdots$">|; 

$key = q/{displaymath}midYmid>kmidymid,hspace{0.1in}midy_nmid>k^nmidymid,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1164.png"
 ALT="\begin{displaymath}
\mid Y\mid &gt; k\mid y\mid, \hspace{0.1in} \mid y_n\mid &gt; k^n\mid y\mid,
\end{displaymath}">|; 

$key = q/midzmidgeqr'>r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1362.png"
 ALT="$\mid z\mid \geq r' &gt; r$">|; 

$key = q/{displaymath}xi=-frac{1}{2},hspace{0.5in}xi>-frac{1}{2},hspace{0.5in}xi<-frac{1}{2}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="318" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="\begin{displaymath}
\xi = -\frac{1}{2}, \hspace{0.5in} \xi &gt; -\frac{1}{2}, \hspace{0.5in} \xi &lt; -\frac{1}{2}
\end{displaymath}">|; 

$key = q/s^{h-1}=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img799.png"
 ALT="$s^{h-1}=1$">|; 

$key = q/{displaymath}zeta^m=frac{2}{m-1},;;;midcmid=frac{1}{m}left(frac{m-1}{2}right)^{1-frac{1}{m}}hspace{0.2in}(midcmid<1).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="421" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img1304.png"
 ALT="\begin{displaymath}
\zeta^m = \frac{2}{m - 1},\;\;\; \mid c\mid = \frac{1}{m}\l...
...{2} \right)^{1 -\frac{1}{m}} \hspace{0.2in} (\mid c\mid &lt; 1).
\end{displaymath}">|; 

$key = q/z_n=e^{inalpha}z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img840.png"
 ALT="$z_n = e^{in\alpha}z$">|; 

$key = q/{displaymath}M_n(rho)>k^nrho,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img851.png"
 ALT="\begin{displaymath}
M_n(\rho) &gt; k^n\rho,
\end{displaymath}">|; 

$key = q/{displaymath}frac{partial}{partialz}[R(z)+lambda]=R'(z),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="\begin{displaymath}\frac{\partial}{\partial z}[R(z) + \lambda] = R'(z),
\end{displaymath}">|; 

$key = q/t^frac{1}{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="25" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img659.png"
 ALT="$t^\frac{1}{p}$">|; 

$key = q/midz_nmid>K_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img583.png"
 ALT="$\mid z_n\mid &gt; K_n$">|; 

$key = q/displaystyleR'(alpha)F_1(z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img421.png"
 ALT="$\displaystyle R'(\alpha)F_1(z),$">|; 

$key = q/z_{4n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img901.png"
 ALT="$z_{4n}$">|; 

$key = q/Q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$Q$">|; 

$key = q/z_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img443.png"
 ALT="$z_2$">|; 

$key = q/z^m+a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1284.png"
 ALT="$z^m + a$">|; 

$key = q/C_{-1}^{(3)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1190.png"
 ALT="$C_{-1}^{(3)}$">|; 

$key = q/C'_{-n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1388.png"
 ALT="$C'_{-n}$">|; 

$key = q/midPhi'(t)mid=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1069.png"
 ALT="$\mid\Phi'(t)\mid = 1$">|; 

$key = q/sigma_{-h};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1118.png"
 ALT="$\sigma_{-h}$">|; 

$key = q/displaystylefrac{Theta_0}{2pi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1152.png"
 ALT="$\displaystyle\frac{\Theta_0}{2\pi}$">|; 

$key = q/C_{-1}^{(1)},C_{-1}^{(2)},dots,C_{-1}^{(d)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1184.png"
 ALT="$C_{-1}^{(1)}, C_{-1}^{(2)},\dots, C_{-1}^{(d)}$">|; 

$key = q/{displaymath}R(z)=f(d.t),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1429.png"
 ALT="\begin{displaymath}
R(z) = f(d.t),
\end{displaymath}">|; 

$key = q/h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$h$">|; 

$key = q/{displaymath}x_n>n(a-mu)-A{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img477.png"
 ALT="\begin{displaymath}
x_n &gt; n(a - \mu) - A
\end{displaymath}">|; 

$key = q/sqrt{Z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1480.png"
 ALT="$\sqrt{Z}$">|; 

$key = q/displaystyleR'_p(alpha_1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$\displaystyle R'_p(\alpha_1)$">|; 

$key = q/textstylegeq;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$\textstyle \geq$">|; 

$key = q/z=left(displaystylefrac{2}{m-1}right)^frac{1}{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="71" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1306.png"
 ALT="$z = \left( \displaystyle\frac{2}{m-1} \right)^\frac{1}{m}$">|; 

$key = q/varepsilon_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img741.png"
 ALT="$\varepsilon_n$">|; 

$key = q/omega;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img458.png"
 ALT="$\omega$">|; 

$key = q/2eta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1170.png"
 ALT="$2\eta$">|; 

$key = q/s=R'(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1353.png"
 ALT="$s = R'(z)$">|; 

$key = q/f(z)-f(z');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1179.png"
 ALT="$f(z) - f(z')$">|; 

$key = q/{displaymath}midR^2(z)z^{m-2}midgeq1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1320.png"
 ALT="\begin{displaymath}
\mid R^2(z)z^{m-2}\mid \geq 1.
\end{displaymath}">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$\textstyle =$">|; 

$key = q/R_{-(n-1)}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img285.png"
 ALT="$R_{-(n-1)}(z)$">|; 

$key = q/T=P(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1509.png"
 ALT="$T = P(t)$">|; 

$key = q/{displaymath}gammarholeft[1+(gamma+1)frac{cos^2omega}{sin^2omega}right],{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img463.png"
 ALT="\begin{displaymath}
\gamma\rho \left[ 1 + (\gamma + 1)\frac{\cos^2\omega}{\sin^2\omega}\right],
\end{displaymath}">|; 

$key = q/rho<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1090.png"
 ALT="$\rho &lt; 1$">|; 

$key = q/{Large{frac{1}{(R'(alpha))};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\Large\frac{1}{(R'(\alpha))}$">|; 

$key = q/{displaymath}R_{q-1}[R(z)]=R[R_{q-1}(z)]{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img255.png"
 ALT="\begin{displaymath}
R_{q-1}[R(z)] = R[R_{q-1}(z)]
\end{displaymath}">|; 

$key = q/sigma_{-a_1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1137.png"
 ALT="$\sigma_{-a_1}$">|; 

$key = q/k>d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1232.png"
 ALT="$k &gt; d$">|; 

$key = q/sqrt{R(w^2)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="49" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1476.png"
 ALT="$\sqrt{R(w^2)}$">|; 

$key = q/dgeq2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$d \geq 2$">|; 

$key = q/midR(z)mid>midzmid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1360.png"
 ALT="$\mid R(z)\mid &gt; \mid z\mid $">|; 

$key = q/A_hneq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img788.png"
 ALT="$A_h \neq 0$">|; 

$key = q/t=Phi(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img398.png"
 ALT="$t = \Phi(z)$">|; 

$key = q/sigma'';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1140.png"
 ALT="$\sigma''$">|; 

$key = q/R_n(z)-z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$R_n(z) - z$">|; 

$key = q/R(z)=Az^d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1115.png"
 ALT="$R( z ) = Az^d$">|; 

$key = q/(lambda,+infty);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1213.png"
 ALT="$(\lambda, +\infty)$">|; 

$key = q/z_{lambda'+mu'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img876.png"
 ALT="$z_{\lambda' + \mu'}$">|; 

$key = q/R_{pq};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img834.png"
 ALT="$R_{pq}$">|; 

$key = q/delta_{-(n-1)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1107.png"
 ALT="$\delta_{-(n-1)}$">|; 

$key = q/l;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1024.png"
 ALT="$l$">|; 

$key = q/-1slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$-1/2$">|; 

$key = q/s_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1253.png"
 ALT="$s_n$">|; 

$key = q/gammageq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img315.png"
 ALT="$\gamma \geq 1$">|; 

$key = q/R(z)=z^d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1407.png"
 ALT="$R(z) = z^d$">|; 

$key = q/{Large{frac{d^n-d}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="$\Large\frac{d^n - d}{2}$">|; 

$key = q/z_1<z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1261.png"
 ALT="$z_1 &lt; z$">|; 

$key = q/x>-A;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img476.png"
 ALT="$x &gt; -A$">|; 

$key = q/R_{-1}^{(0)},R_{-1}^{(1)},dots,R_{-1}^{(d-1)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1339.png"
 ALT="$R_{-1}^{(0)}, R_{-1}^{(1)}, \dots, R_{-1}^{(d-1)}$">|; 

$key = q/{displaymath}z_n=z+na+theta_nn^{1-gamma}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="31" BORDER="0"
 SRC="|."$dir".q|img490.png"
 ALT="\begin{displaymath}
z_n = z + na + \theta_nn^{1-\gamma}
\end{displaymath}">|; 

$key = q/{displaymath}frac{partial}{partialz}[R_n(z,lambda)-z]{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="\begin{displaymath}\frac{\partial}{\partial z}[R_n(z, \lambda) - z] \end{displaymath}">|; 

$key = q/s_1,s_2,dots,s_n,dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1250.png"
 ALT="$s_1, s_2, \dots, s_n, \dots$">|; 

$key = q/(alpha_1),(alpha_1alpha_2),dots,(alpha_1alpha_2dotsalpha_n),dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1418.png"
 ALT="$(\alpha_1), (\alpha_1 \alpha_2), \dots, (\alpha_1 \alpha_2 \dots \alpha_n),\dots$">|; 

$key = q/(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img220.png"
 ALT="$(z)$">|; 

$key = q/displaystylez=frac{1-w^2}{1+w^2}=cosvarphi,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1516.png"
 ALT="$\displaystyle z = \frac{1-w^2}{1 + w^2} = \cos\varphi,$">|; 

$key = q/{displaymath}F[R_{-1}(z)]=frac{1}{s}F(z),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img859.png"
 ALT="\begin{displaymath}
F[R_{-1}(z)] = \frac{1}{s}F(z),
\end{displaymath}">|; 

$key = q/delta_1,delta_2,dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img411.png"
 ALT="$\delta_1, \delta_2, \dots$">|; 

$key = q/z_{-1}';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1183.png"
 ALT="$z_{-1}'$">|; 

$key = q/overline{omega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="$\overline{\omega}$">|; 

$key = q/{calL}n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img497.png"
 ALT="${\cal L}n$">|; 

$key = q/d-1geq1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img963.png"
 ALT="$d-1 \geq 1$">|; 

$key = q/p=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img682.png"
 ALT="$p = 2$">|; 

$key = q/{displaymath}F(z_1)=z_1+o({calL}midz_1mid),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img592.png"
 ALT="\begin{displaymath}
F(z_1) = z_1 + o({\cal L}\mid z_1\mid ),
\end{displaymath}">|; 

$key = q/sumchi(z_i);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img524.png"
 ALT="$\sum\chi(z_i)$">|; 

$key = q/z_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$z_1$">|; 

$key = q/{displaymath}array{{ll}F(f(z))=lambdaF(z)&hspace{2.0cm}mbox{ecuaci'ondeSchr"oder}array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="417" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img397.png"
 ALT="\begin{displaymath}
\begin{array}{ll}
F(f(z)) = \lambda F(z) &amp; \hspace{2.0cm} \mbox{ecuaci\'on de Schr\uml oder} \\\\
\end{array}\end{displaymath}">|; 

$key = q/{calA}_(-n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1221.png"
 ALT="${\cal A}_(-n)$">|; 

$key = q/n=4,p=3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img342.png"
 ALT="$n = 4, p = 3$">|; 

$key = q/displaystylesigma;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\displaystyle \sigma$">|; 

$key = q/(d-1)+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1406.png"
 ALT="$(d-1)+1$">|; 

$key = q/{displaymath}rho+frac{1}{Q(z)}=frac{A}{(z-overline{omega})^h}+B,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img239.png"
 ALT="\begin{displaymath}
\rho + \frac{1}{Q(z)} = \frac{A}{(z - \overline{\omega})^h} + B,
\end{displaymath}">|; 

$key = q/gamma=d;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img316.png"
 ALT="$\gamma = d$">|; 

$key = q/{displaymath}array{{lc}t_1=t+pa+thetafrac{pa}{2},&t_2=t_1+pa+theta_1frac{pa}{2},eq1,t_n=t_{n-1}+pa+theta_{n-1}frac{pa}{2};array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="107" BORDER="0"
 SRC="|."$dir".q|img769.png"
 ALT="\begin{displaymath}
\begin{array}{lc}
t_1 = t + pa + \theta\frac{pa}{2}, &amp; \\\\
t...
... \\\\
t_n = t_{n-1} + pa + \theta_{n-1}\frac{pa}{2};
\end{array}\end{displaymath}">|; 

$key = q/A_hz^h;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img789.png"
 ALT="$A_hz^h$">|; 

$key = q/(z-overline{omega});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img242.png"
 ALT="$(z-\overline{\omega})$">|; 

$key = q/delta_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img416.png"
 ALT="$\delta_n$">|; 

$key = q/gamma,gamma',gamma'',...;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img332.png"
 ALT="$\gamma, \gamma', \gamma'', ...$">|; 

$key = q/displaystylefrac{A}{y};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img934.png"
 ALT="$\displaystyle\frac{A}{y}$">|; 

$key = q/Delta_{(1)},Delta_{(2)},dots,Delta_{(p)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img729.png"
 ALT="$\Delta_{(1)}, \Delta_{(2)}, \dots, \Delta_{(p)}$">|; 

$key = q/displaystylefrac{a^2+b^2}{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1071.png"
 ALT="$\displaystyle\frac{a^2 + b^2}{A}$">|; 

$key = q/n+1,;n+2,;n+3,;dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1206.png"
 ALT="$n + 1,\; n + 2,\; n + 3,\; \dots$">|; 

$key = q/z_1,z_2,...,z_n,...;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$z_1, z_2, ..., z_n, ...$">|; 

$key = q/(-1,+1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1504.png"
 ALT="$(-1, +1)$">|; 

$key = q/Z=R(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img228.png"
 ALT="$Z = R(z)$">|; 

$key = q/R'(y)=+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img994.png"
 ALT="$R'(y) = + 1$">|; 

$key = q/R(w);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img721.png"
 ALT="$R(w)$">|; 

$key = q/t_1=t^q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img399.png"
 ALT="$t_1 = t^q$">|; 

$key = q/C_{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1194.png"
 ALT="$C_{-2}$">|; 

$key = q/midR'(z)midleqK;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1371.png"
 ALT="$\mid R'(z)\mid \leq K$">|; 

$key = q/p+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img740.png"
 ALT="$p+1$">|; 

$key = q/lambda_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img330.png"
 ALT="$\lambda_3$">|; 

$key = q/frac{Theta}{aK}sum_1^inftydisplaystylefrac{{calL}n}{n^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img545.png"
 ALT="$\frac{\Theta}{aK}\sum_1^\infty \displaystyle\frac{{\cal L}n}{n^2}$">|; 

$key = q/p<q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1148.png"
 ALT="$p &lt; q$">|; 

$key = q/s_i>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1008.png"
 ALT="$s_i &gt; 1$">|; 

$key = q/R_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1478.png"
 ALT="$R_1$">|; 

$key = q/z_1-alpha=s(z-alpha)+R(z-alpha)^2+cdots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$z_1 - \alpha = s(z - \alpha) + R(z - \alpha)^2 + \cdots$">|; 

$key = q/2pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img782.png"
 ALT="$2\pi$">|; 

$key = q/displaystyleMgeq0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="$\displaystyle M \geq 0.$">|; 

$key = q/midtmid-M>r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1364.png"
 ALT="$\mid t\mid - M &gt; r$">|; 

$key = q/delta_{-n'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1405.png"
 ALT="$\delta_{-n'}$">|; 

$key = q/alpha_h=alpha_k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$\alpha_h = \alpha_k$">|; 

$key = q/D_1,D_2,...;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img335.png"
 ALT="$D_1, D_2, ...$">|; 

$key = q/z_lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img867.png"
 ALT="$z_\lambda$">|; 

$key = q/R(z)=z+frac{1}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img758.png"
 ALT="$R(z) = z + \frac{1}{z}$">|; 

$key = q/>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$&gt; 1$">|; 

$key = q/u_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img511.png"
 ALT="$u_n$">|; 

$key = q/H;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img794.png"
 ALT="$H$">|; 

$key = q/R(z)-z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$R(z) - z$">|; 

$key = q/{displaymath}z_n=w_n+mu_2w_n^2+cdots+mu_pw_n^p+mu_{p+1}w_n^{p+1}+cdots{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="381" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img736.png"
 ALT="\begin{displaymath}
z_n = w_n + \mu_2w_n^2 + \cdots + \mu_pw_n^p + \mu_{p+1}w_n^{p+1} + \cdots
\end{displaymath}">|; 

$key = q/displaystyleoverline{omega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img262.png"
 ALT="$\displaystyle \overline{\omega}$">|; 

$key = q/{calA}_p{calA}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1226.png"
 ALT="${\cal A}_p {\cal A}_1$">|; 

$key = q/U_n(z)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img917.png"
 ALT="$U_n(z) = 0$">|; 

$key = q/G(ngeq1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img366.png"
 ALT="$G (n \geq 1) $">|; 

$key = q/n=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$n = 2$">|; 

$key = q/{Large{frac{1}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$\Large\frac{1}{z}$">|; 

$key = q/h=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1490.png"
 ALT="$h=0$">|; 

$key = q/{Large{frac{d^n-d}{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$\Large\frac{d^n - d}{n}$">|; 

$key = q/3^0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img598.png"
 ALT="$3^0$">|; 

$key = q/h-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img801.png"
 ALT="$h-1$">|; 

$key = q/psi(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img434.png"
 ALT="$\psi(z)$">|; 

$key = q/displaystylefrac{varepsilon_n}{t_n^{1+frac{1}{p}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img743.png"
 ALT="$\displaystyle\frac{\varepsilon_n}{t_n^{1 + \frac{1}{p}}}$">|; 

$key = q/ML;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img464.png"
 ALT="$ML$">|; 

$key = q/(t^p=z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img684.png"
 ALT="$(t^p = z)$">|; 

$key = q/{displaymath}P(t)=e^{ia}t^m;;;;;;mbox{{a{real,{m{entero{>0{}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="310" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1512.png"
 ALT="\begin{displaymath}
P(t) = e^{ia}t^m \;\;\;\;\;\; \mbox{ $a$ real, $m$ entero $&gt; 0$}.
\end{displaymath}">|; 

$key = q/rho=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img878.png"
 ALT="$\rho = $">|; 

$key = q/R(z_n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img773.png"
 ALT="$R(z_n)$">|; 

$key = q/2pidisplaystylefrac{p}{q};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1146.png"
 ALT="$2\pi\displaystyle\frac{p}{q}$">|; 

$key = q/{displaymath}midR'(z)mid>K>1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1309.png"
 ALT="\begin{displaymath}
\mid R'(z)\mid &gt; K &gt; 1.
\end{displaymath}">|; 

$key = q/w=a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1473.png"
 ALT="$w=a$">|; 

$key = q/3^{textstylefrac{1}{d-1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1377.png"
 ALT="$3^{\textstyle\frac{1}{d-1}}$">|; 

$key = q/{displaymath}z_1=z+frac{k}{z^{q-1}}+...{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="\begin{displaymath}
z_1 = z + \frac{k}{z^{q-1}} + ...
\end{displaymath}">|; 

$key = q/{displaymath}Releft(frac{1}{s-1}right)+Releft(frac{1}{s'-1}right)+1+P=0hspace{0.3in}(P>0){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="400" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img964.png"
 ALT="\begin{displaymath}
\Re\left( \frac{1}{s-1} \right) + \Re\left( \frac{1}{s'-1} \right) + 1 + P = 0 \hspace{0.3in} ( P &gt; 0)
\end{displaymath}">|; 

$key = q/x>A;(A>r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img517.png"
 ALT="$x &gt; A \;(A &gt; r)$">|; 

$key = q/{displaymath}Phi[R(z)]=Phi^q(z).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img396.png"
 ALT="\begin{displaymath}
\Phi[R(z)] = \Phi^q(z).
\end{displaymath}">|; 

$key = q/R(w^2);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1467.png"
 ALT="$R(w^2)$">|; 

$key = q/Delta[R(t)>A];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img715.png"
 ALT="$\Delta[R(t) &gt; A]$">|; 

$key = q/(alpha_1,alpha_2,dots,alpha_n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1402.png"
 ALT="$(\alpha_1, \alpha_2, \dots, \alpha_n)$">|; 

$key = q/{displaymath}s=1,hspace{0.2in}R''(alpha),hspace{0.2in}dots,hspace{0.2in}R^{(p)}(alpha)=0,hspace{0.2in}R^{p+1}(alpha)neq0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="440" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img641.png"
 ALT="\begin{displaymath}
s = 1, \hspace{0.2in} R''(\alpha), \hspace{0.2in} \dots, \hs...
...n} R^{(p)}(\alpha) = 0, \hspace{0.2in} R^{p+1}(\alpha) \neq 0.
\end{displaymath}">|; 

$key = q/rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img236.png"
 ALT="$\rho$">|; 

$key = q/M(r);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img778.png"
 ALT="$M(r)$">|; 

$key = q/{displaymath}R(z)=frac{A}{(z-overline{omega})^h}+overline{omega}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img264.png"
 ALT="\begin{displaymath}
R(z) = \frac{A}{(z - \overline{\omega})^h} + \overline{\omega}
\end{displaymath}">|; 

$key = q/(a_j,a_{j+1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img953.png"
 ALT="$(a_j, a_{j+1})$">|; 

$key = q/1slashz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img528.png"
 ALT="$1/z$">|; 

$key = q/3^{k-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1197.png"
 ALT="$3^{k-1}$">|; 

$key = q/{displaymath}R(z)=frac{z^2}{z^3+2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img1328.png"
 ALT="\begin{displaymath}
R(z) = \frac{z^2}{z^3 + 2}.
\end{displaymath}">|; 

$key = q/D_{(1)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img730.png"
 ALT="$D_{(1)}$">|; 

$key = q/d^n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$d^n$">|; 

$key = q/{displaymath}F(z_1)=F[R(z)]=F(z)+a{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img514.png"
 ALT="\begin{displaymath}
F(z_1) = F[R(z)] = F(z) + a
\end{displaymath}">|; 

$key = q/{displaymath}prod_{p=0}^{n-1}left(1-frac{C'}{midz_imid^h}right)<midR'_n(z)mid<prod_{0}^{n-1}left(1+frac{C}{midz_imid^h}right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="386" HEIGHT="60" BORDER="0"
 SRC="|."$dir".q|img571.png"
 ALT="\begin{displaymath}
\prod_{p=0}^{n-1}\left( 1 - \frac{C'}{\mid z_i\mid ^h} \righ...
... &lt; \prod_{0}^{n-1}\left( 1 + \frac{C}{\mid z_i\mid ^h} \right)
\end{displaymath}">|; 

$key = q/displaystylefrac{-1sqrt{2}}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img898.png"
 ALT="$\displaystyle\frac{-1\sqrt{2}}{2}$">|; 

$key = q/1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$1$">|; 

$key = q/-displaystylefrac{pi}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1317.png"
 ALT="$-\displaystyle\frac{\pi}{2}$">|; 

$key = q/P_n(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img910.png"
 ALT="$P_n(a)$">|; 

$key = q/R'(zeta)=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1381.png"
 ALT="$R'(\zeta) = $">|; 

$key = q/displaystyle{sl{frac{1}{s-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img979.png"
 ALT="$\displaystyle\sl\frac{1}{s-1}$">|; 

$key = q/z^p=t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img772.png"
 ALT="$z^p = t$">|; 

$key = q/{displaymath}F(z)=lim_{n=infty}left[z_n-frac{b}{a}{calL}n-naright].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img521.png"
 ALT="\begin{displaymath}
F(z) = \lim_{n=\infty}\left[ z_n - \frac{b}{a}{\cal L}n - na \right].
\end{displaymath}">|; 

$key = q/{displaymath}z_{-1}=R_{-1}(z)=z+az^{p+1}+cdots,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img675.png"
 ALT="\begin{displaymath}
z_{-1} = R_{-1}(z) = z + az^{p+1} + \cdots,
\end{displaymath}">|; 

$key = q/alpha=ci;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1500.png"
 ALT="$\alpha = ci$">|; 

$key = q/displaystyle(s^n-1)(z-alpha);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$\displaystyle (s^n - 1)(z - \alpha)$">|; 

$key = q/{displaymath}array{{cc}R(a_{-2})=a_{-1},&R(b_{-2})=b_{-1};array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1444.png"
 ALT="\begin{displaymath}\begin{array}{cc}
R(a_{-2}) = a_{-1}, &amp; R(b_{-2}) = b_{-1};
\end{array}\end{displaymath}">|; 

$key = q/{displaymath}f(t_1)=sf(t);;;mbox{dedonde};;;t_1=F[sf(t)].{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="321" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img826.png"
 ALT="\begin{displaymath}
f(t_1) = sf(t) \;\;\; \mbox{de donde} \; \;\;t_1 = F[sf(t)].
\end{displaymath}">|; 

$key = q/f(st)=sf(t);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img827.png"
 ALT="$f(st) = sf(t)$">|; 

$key = q/{displaymath}sum^{d+1}_{1}frac{1}{s-1}+1=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="\begin{displaymath}
\sum^{d+1}_{1} \frac{1}{s-1} + 1 = 0.
\end{displaymath}">|; 

$key = q/1+frac{1}{K};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1072.png"
 ALT="$1 + \frac{1}{K}$">|; 

$key = q/Q(0)=0,Q'(0)=e^{ialpha};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img845.png"
 ALT="$Q(0)=0, Q'(0) = e^{i\alpha}$">|; 

$key = q/varphi(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\varphi(z)$">|; 

$key = q/{displaymath}z_1=R(z)=z+a_{p+1}z^{p+1}+a_{p+2}z^{p+2}+cdots+a_{2p}z^{2p}+a_{2p+1}z^{2p+1}+cdots{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="554" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img685.png"
 ALT="\begin{displaymath}
z_1 = R(z) = z + a_{p+1}z^{p+1} + a_{p+2}z^{p+2} + \cdots + a_{2p}z^{2p} + a_{2p+1}z^{2p+1} + \cdots
\end{displaymath}">|; 

$key = q/(C,C_{-1}),(C_{-1},{C'}_{-1}),({C'}_{-1},C');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1435.png"
 ALT="$(C, C_{-1}), (C_{-1}, {C'}_{-1}), ({C'}_{-1}, C')$">|; 

$key = q/{displaymath}array{{rcl}z&=&t^{frac{1}{p}},z_1&=&t_1^{frac{1}{p}},array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="66" BORDER="0"
 SRC="|."$dir".q|img646.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
z &amp; = &amp; t^{\frac{1}{p}}, \\\\
z_1 &amp; = &amp; t_1^{\frac{1}{p}},
\end{array}\end{displaymath}">|; 

$key = q/R(z)+lambda=z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$R(z) + \lambda = z$">|; 

$key = q/displaystylefrac{Cz+C'}{(z-a)^2+b^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1005.png"
 ALT="$\displaystyle\frac{Cz + C'}{(z - a)^2 + b^2}$">|; 

$key = q/z,z_1,z_2,dots,z_n,dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img670.png"
 ALT="$z, z_1, z_2, \dots, z_n, \dots$">|; 

$key = q/x>;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img535.png"
 ALT="$x &gt;$">|; 

$key = q/Phi^{(2)}(t)=t;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1053.png"
 ALT="$\Phi^{(2)}(t) = t$">|; 

$key = q/{displaymath}mid{logH(z_n)}mid<2Amid{z_n}mid.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img387.png"
 ALT="\begin{displaymath}
\mid {\log H(z_n)}\mid &lt; 2A\mid {z_n}\mid .
\end{displaymath}">|; 

$key = q/midz_1mid>midzmid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img530.png"
 ALT="$\mid z_1\mid &gt;  \mid z\mid $">|; 

$key = q/displaystylefrac{R(z)}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1077.png"
 ALT="$\displaystyle\frac{R(z)}{z}$">|; 

$key = q/y_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img612.png"
 ALT="$y_3$">|; 

$key = q/alpha_1,alpha_2,dots,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img412.png"
 ALT="$\alpha_1, \alpha_2, \dots $">|; 

$key = q/{displaymath}midz_1mid=midR(z)midgeqmidtmid-M.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1363.png"
 ALT="\begin{displaymath}
\mid z_1\mid = \mid R(z)\mid \geq \mid t\mid - M.
\end{displaymath}">|; 

$key = q/R_n(z)=z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$R_n(z) = z$">|; 

$key = q/displaystylefrac{1}{q};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1147.png"
 ALT="$\displaystyle\frac{1}{q}$">|; 

$key = q/aneq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1488.png"
 ALT="$a \neq 0$">|; 

$key = q/R_{q-1}(z)=overline{omega}+{Large{frac{1}{P(z)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img230.png"
 ALT="$R_{q-1}(z) = \overline{\omega} + \Large\frac{1}{P(z)}$">|; 

$key = q/{displaymath}S_{p+q-1}(a_{-p})=S_{p+q-1}(a_{-p-q}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="237" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="\begin{displaymath}
S_{p+q-1}(a_{-p}) = S_{p+q-1}(a_{-p-q}).
\end{displaymath}">|; 

$key = q/D,Delta,D',Delta';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img681.png"
 ALT="$D, \Delta, D', \Delta'$">|; 

$key = q/{calD};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img442.png"
 ALT="${\cal D}$">|; 

$key = q/F'(z)=1+o(frac{1}{z});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img586.png"
 ALT="$F'(z) = 1 + o(\frac{1}{z})$">|; 

$key = q/n^{mbox{{scriptsize{{'esimo}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1231.png"
 ALT="$n^{\mbox{\scriptsize {\'esimo}}}$">|; 

$key = q/lambda(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1061.png"
 ALT="$\lambda(z)$">|; 

$key = q/R'(z)=2z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1271.png"
 ALT="$R'(z) = 2z$">|; 

$key = q/C_{-1}^{(2)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1186.png"
 ALT="$C_{-1}^{(2)}$">|; 

$key = q/r';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1370.png"
 ALT="$r'$">|; 

$key = q/{displaymath}array{{rcl}R_{n_1}(z')&=&xi',R_{n_2}(z'')&=&xi'',&vdots&R_{n_p}[z^{(p)}]&=&xi^{(p)}.array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="107" BORDER="0"
 SRC="|."$dir".q|img1084.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
R_{n_1}(z') &amp; = &amp; \xi', \\\\
R_{n_2}(z'') ...
... \\\\
&amp;\vdots &amp;\\\\
R_{n_p}[z^{(p)}] &amp; = &amp; \xi^{(p)}.
\end{array}\end{displaymath}">|; 

$key = q/{displaymath}frac{1}{s-1}+frac{1}{s'+1}+sum_1^{d-1}frac{1}{s_i-1}+1=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="283" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img959.png"
 ALT="\begin{displaymath}
\frac{1}{s-1} + \frac{1}{s' + 1} + \sum_1^{d-1}\frac{1}{s_i - 1} + 1 = 0
\end{displaymath}">|; 

$key = q/{displaymath}F[R(z)]=F(z)+a.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img639.png"
 ALT="\begin{displaymath}
F[R(z)] = F(z) + a.
\end{displaymath}">|; 

$key = q/{displaymath}nsum^{frac{d^n-d}{n}}_{1}frac{1}{t-1}+sum^{d+1}_{1}frac{1}{s^n-1}+1=0,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="67" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="\begin{displaymath}
n\sum^{\frac{d^n - d}{n}}_{1}\frac{1}{t-1} + \sum^{d + 1}_{1}\frac{1}{s^n - 1} + 1 = 0,
\end{displaymath}">|; 

$key = q/p'<p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1228.png"
 ALT="$p'&lt;p$">|; 

$key = q/varepsilon>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img482.png"
 ALT="$\varepsilon &gt; 0$">|; 

$key = q/displaystylefrac{1-isqrt{19}}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img884.png"
 ALT="$\displaystyle\frac{1 - i\sqrt{19}}{2}$">|; 

$key = q/{displaymath}Y_1=Q(A,y_1)=Q(A,y_2)hspace{0.3in}(y_1<y_2){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="312" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img611.png"
 ALT="\begin{displaymath}
Y_1 = Q(A, y_1) = Q(A, y_2) \hspace{0.3in} (y_1 &lt; y_2)
\end{displaymath}">|; 

$key = q/Z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img601.png"
 ALT="$Z$">|; 

$key = q/S(z)=infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="$S(z) = \infty$">|; 

$key = q/delta_{-n-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1114.png"
 ALT="$\delta_{-n-1}$">|; 

$key = q/w=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img724.png"
 ALT="$w = $">|; 

$key = q/left(frac{pi}{p}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img674.png"
 ALT="$\left( \frac{\pi}{p} \right)$">|; 

$key = q/midR'(z)midleqK;(K>1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1357.png"
 ALT="$\mid R'(z)\mid \leq K \;(K &gt; 1)$">|; 

$key = q/displaystyleh+sum_1^{d-1}frac{1}{s_i-1}+1=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1023.png"
 ALT="$\displaystyle h + \sum_1^{d - 1}\frac{1}{s_i - 1} + 1 = 0.$">|; 

$key = q/R_{-h}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1117.png"
 ALT="$R_{-h}(z)$">|; 

$key = q/{displaymath}z=Alambda^{frac{1}{q}}+Blambda^{frac{2}{q}}+cdots{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="\begin{displaymath}
z = A\lambda^{\frac{1}{q}} + B\lambda^{\frac{2}{q}} + \cdots
\end{displaymath}">|; 

$key = q/z=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1307.png"
 ALT="$z = 1$">|; 

$key = q/midtmid>L;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1369.png"
 ALT="$\mid t\mid &gt; L$">|; 

$key = q/{displaymath}frac{C}{(z-rho)^k}+D=overline{omega}+frac{1}{P(z)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img249.png"
 ALT="\begin{displaymath}
\frac{C}{(z - \rho)^k} + D = \overline{\omega} + \frac{1}{P(z)}.
\end{displaymath}">|; 

$key = q/{displaymath}t_1=S(t)=t+pa+frac{b}{t}+frac{c}{t^{1+frac{1}{p}}}+cdots.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img710.png"
 ALT="\begin{displaymath}
t_1 = S(t) = t + pa + \frac{b}{t} + \frac{c}{t^{1 + \frac{1}{p}}} + \cdots.
\end{displaymath}">|; 

$key = q/f'(alpha)>0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img957.png"
 ALT="$f'(\alpha) &gt; 0$">|; 

$key = q/{Large{frac{1}{s^n-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$\Large\frac{1}{s^n - 1}$">|; 

$key = q/t,t_1,dots,t_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img768.png"
 ALT="$t, t_1, \dots, t_n$">|; 

$key = q/{displaymath}F(z)=z+o({calL}midzmid),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img518.png"
 ALT="\begin{displaymath}
F(z) = z + o({\cal L}\mid z\mid ),
\end{displaymath}">|; 

$key = q/<1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1296.png"
 ALT="$&lt;1$">|; 

$key = q/(C,C_{-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1440.png"
 ALT="$(C, C_{-1})$">|; 

$key = q/delta_{-n'},;(n'>n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1404.png"
 ALT="$\delta_{-n'},\;(n' &gt; n)$">|; 

$key = q/{displaymath}S_{p+q-1}(a_{-p-q})=a_{-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="\begin{displaymath}S_{p+q-1}(a_{-p-q}) = a_{-1}. \end{displaymath}">|; 

$key = q/left(omega=e^frac{2ikpi}{p}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img726.png"
 ALT="$\left( \omega = e^\frac{2ik\pi}{p} \right) $">|; 

$key = q/{displaymath}z_1=R(z),hspace{0.2in}z_2=R(z_1),hspace{0.2in}dots,hspace{0.2in}z_n=R(z_{n-1}),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="396" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img669.png"
 ALT="\begin{displaymath}
z_1 = R(z), \hspace{0.2in} z_2 = R(z_1), \hspace{0.2in} \dots, \hspace{0.2in} z_n = R(z_{n-1}),
\end{displaymath}">|; 

$key = q/C_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1177.png"
 ALT="$C_1$">|; 

$key = q/R_n(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$R_n(z)$">|; 

$key = q/{displaymath}Z=zleft[k-sumfrac{2A}{z-a^2},right]^2=R(z).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1494.png"
 ALT="\begin{displaymath}
Z = z\left[ k - \sum\frac{2A}{z - a^2}, \right]^2 = R(z).
\end{displaymath}">|; 

$key = q/{displaymath}a,a_{-1},a_{-2},dots,a_{-n},dots,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="\begin{displaymath}
a, a_{-1}, a_{-2}, \dots, a_{-n}, \dots,
\end{displaymath}">|; 

$key = q/R_1(w);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1491.png"
 ALT="$R_1(w)$">|; 

$key = q/{displaymath}t_n=F[R_n(z)]=s^nt.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img363.png"
 ALT="\begin{displaymath}
t_n = F[R_n(z)] = s^nt.
\end{displaymath}">|; 

$key = q/z^{p+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img693.png"
 ALT="$z^{p+1}$">|; 

$key = q/b=R(b);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1245.png"
 ALT="$b = R(b)$">|; 

$key = q/w_1=P(z_1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img706.png"
 ALT="$w_1 = P(z_1)$">|; 

$key = q/R,R_2,...,R_n,...;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$R, R_2, ..., R_n, ...$">|; 

$key = q/displaystylefrac{1}{s};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img857.png"
 ALT="$\displaystyle\frac{1}{s}$">|; 

$key = q/Z=R_p(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$Z = R_p(z)$">|; 

$key = q/summida_{-n}-a_{-(n-1)}mid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1451.png"
 ALT="$\sum\mid a_{-n} - a_{-(n-1)}\mid $">|; 

$key = q/displaystyle2>0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="$\displaystyle 2 &gt; 0.$">|; 

$key = q/{displaymath}frac{1}{R(z)-z}=sumfrac{1}{s-1}frac{1}{z-alpha}+sumprimeleft[frac{az-beta)^{q-1}}+cdots+frac{a_{-1}}{z-beta}right],{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="591" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="\begin{displaymath}
\frac{1}{R(z)-z} = \sum\frac{1}{s-1}\frac{1}{z-\alpha} + \su...
...}}{(z-\beta)^{q-1}} + \cdots + \frac{a_{-1}}{z-\beta} \right],
\end{displaymath}">|; 

$key = q/theta_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img491.png"
 ALT="$\theta_n$">|; 

$key = q/M'L';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img465.png"
 ALT="$M'L'$">|; 

$key = q/{displaymath}frac{l}{(z-alpha)^2}+frac{h}{z-alpha}+sum_1^{d-1}frac{1}{(s_i-1)}frac{1}{(z-alpha_i)}+frac{1}{z-A}=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="433" HEIGHT="58" BORDER="0"
 SRC="|."$dir".q|img1028.png"
 ALT="\begin{displaymath}
\frac{l}{(z - \alpha)^2} + \frac{h}{z - \alpha} + \sum_1^{d ...
...ac{1}{(s_i - 1)}\frac{1}{(z - \alpha_i)} + \frac{1}{z - A} = 0
\end{displaymath}">|; 

$key = q/displaystylec',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img281.png"
 ALT="$\displaystyle c',$">|; 

$key = q/a_{-p}=a_{-p-q};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="$a_{-p} = a_{-p-q}$">|; 

$key = q/{displaymath}R_{q-1}(z)=overline{omega}+frac{1}{P(z)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img219.png"
 ALT="\begin{displaymath}
R_{q-1}(z) = \overline{\omega} + \frac{1}{P(z)}.
\end{displaymath}">|; 

$key = q/C_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1275.png"
 ALT="$C_n$">|; 

$key = q/{displaymath}R_n(z)=z-naz^{p+1}+bz^{p+2}+cdots.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="278" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img777.png"
 ALT="\begin{displaymath}
R_n(z) = z - naz^{p+1} + bz^{p+2} + \cdots.
\end{displaymath}">|; 

$key = q/2mu;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img445.png"
 ALT="$2\mu$">|; 

$key = q/z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="$z= 0$">|; 

$key = q/v;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1095.png"
 ALT="$v$">|; 

$key = q/sqrt{z-5};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1281.png"
 ALT="$\sqrt{z - 5}$">|; 

$key = q/delta_{-1}^{(0)},delta_{-1}^{(1)},delta_{-1}^{(2)},dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1396.png"
 ALT="$\delta_{-1}^{(0)}, \delta_{-1}^{(1)}, \delta_{-1}^{(2)}, \dots$">|; 

$key = q/alpha_i;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1002.png"
 ALT="$\alpha_i$">|; 

$key = q/displaystylefrac{p}{2pi};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img677.png"
 ALT="$\displaystyle\frac{p}{2\pi}$">|; 

$key = q/displaystylesum^{d}_{1}left(frac{1}{s-1}right)+frac{1}{s'-1}+1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$\displaystyle \sum^{d}_{1}\left(\frac{1}{s-1}\right) + \frac{1}{s' - 1} + 1$">|; 

$key = q/x_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img479.png"
 ALT="$x_n$">|; 

$key = q/Lambda_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img493.png"
 ALT="$\Lambda_n$">|; 

$key = q/{displaymath}A=mbox{const}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img243.png"
 ALT="\begin{displaymath}
A = \mbox{const}.
\end{displaymath}">|; 

$key = q/{displaymath}left{array{{l}X=kx+h-sumfrac{A(x-a)}{(x-a)^2+y^2}Y=ky+sumfrac{Ay}{(x-a)^2+y^2}.array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="64" BORDER="0"
 SRC="|."$dir".q|img1163.png"
 ALT="\begin{displaymath}
\left\{
\begin{array}{l}
X = kx + h - \sum\frac{A(x - a)}{(x...
...\
Y = ky + \sum\frac{Ay}{(x - a)^2 + y^2}.
\end{array}\right.
\end{displaymath}">|; 

$key = q/n^0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img516.png"
 ALT="$n^0$">|; 

$key = q/P(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img218.png"
 ALT="$P(z)$">|; 

$key = q/(midz-alphamidleqrho);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img847.png"
 ALT="$(\mid z-\alpha\mid \leq \rho)$">|; 

$key = q/w^{hp+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img752.png"
 ALT="$w^{hp+1}$">|; 

$key = q/{displaymath}F(z)=frac{1}{z}+oleft(logmidfrac{1}{z}midright).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img640.png"
 ALT="\begin{displaymath}
F(z) = \frac{1}{z} + o\left(\log \mid\frac{1}{z}\mid\right).
\end{displaymath}">|; 

$key = q/displaystylefrac{1}{Nq};(N=1,2,3,dots);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1149.png"
 ALT="$\displaystyle\frac{1}{Nq}\;(N = 1, 2, 3, \dots)$">|; 

$key = q/{displaymath}d_{-n}sigma<frac{1}{k'}d_{-(n-1)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1203.png"
 ALT="\begin{displaymath}
d_{-n}\sigma &lt; \frac{1}{k'}d_{-(n-1)}.
\end{displaymath}">|; 

$key = q/u<-frac{1}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img967.png"
 ALT="$u &lt; -\frac{1}{2}$">|; 

$key = q/displaystyle0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$\displaystyle 0,$">|; 

$key = q/alpha,beta,gamma,delta,dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1154.png"
 ALT="$\alpha, \beta, \gamma, \delta, \dots $">|; 

$key = q/u_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img331.png"
 ALT="$u_3$">|; 

$key = q/{displaymath}array{{l}Re(t_n)=Re(t)+npa+ntheta''frac{pa}{2}hspace{0.3in}midtheta''midleq1,Re(t_n)>Re(t)+nfrac{pa}{2}.array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="345" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img771.png"
 ALT="\begin{displaymath}
\begin{array}{l}
\Re(t_n) = \Re(t) + npa + n\theta''\frac{pa...
...id \leq 1, \\\\
\Re(t_n) &gt; \Re(t) + n\frac{pa}{2}.
\end{array}\end{displaymath}">|; 

$key = q/2^0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img597.png"
 ALT="$2^0$">|; 

$key = q/{displaymath}z=f(t),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1426.png"
 ALT="\begin{displaymath}
z = f(t),
\end{displaymath}">|; 

$key = q/displaystylefrac{N}{d^n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1424.png"
 ALT="$\displaystyle\frac{N}{d^n}$">|; 

$key = q/M_n(rho);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img852.png"
 ALT="$M_n(\rho)$">|; 

$key = q/displaystylealpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$\displaystyle \alpha$">|; 

$key = q/{displaymath}z_1-z=R(z)-z=h-sumfrac{A}{z-a}>0hspace{0.2in}(z<z_1),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="405" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1244.png"
 ALT="\begin{displaymath}
z_1 - z = R(z) - z = h - \sum\frac{A}{z-a} &gt; 0 \hspace{0.2in}(z &lt; z_1),
\end{displaymath}">|; 

$key = q/r<rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img779.png"
 ALT="$r &lt; \rho$">|; 

$key = q/{displaymath}array{{rcccl}t_1^{frac{1}{p}}&=&t^frac{1}{p}left(1+frac{a}{t}+frac{&t+pa+frac{pb}{t^frac{1}{p}}+cdots&=&S(t).array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="502" HEIGHT="115" BORDER="0"
 SRC="|."$dir".q|img647.png"
 ALT="\begin{displaymath}
\begin{array}{rcccl}
t_1^{\frac{1}{p}} &amp; = &amp; t^\frac{1}{p}\l...
... pa + \frac{pb}{t^\frac{1}{p}} + \cdots &amp; = &amp; S(t).
\end{array}\end{displaymath}">|; 

$key = q/textstyleR_{p+q}(a_{-p+q})=a,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="$\textstyle R_{p+q}(a_{-p+q}) = a,$">|; 

$key = q/psi(z),psi(z_1),psi(z_2),dots;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img469.png"
 ALT="$\psi(z), \psi(z_1), \psi(z_2), \dots$">|; 

$key = q/sumxileq-frac{3}{2}<-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\sum \xi \leq -\frac{3}{2} &lt; -1$">|; 

$key = q/M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1358.png"
 ALT="$M$">|; 

$key = q/pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img838.png"
 ALT="$\pi$">|; 

$key = q/(a_{-i},a_{-(i+1)});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1448.png"
 ALT="$(a_{-i}, a_{-(i+1)})$">|; 

$key = q/a^{d^{n-1}-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="22" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img911.png"
 ALT="$a^{d^{n-1}-1}$">|; 

$key = q/{displaymath}array{{cccc}(0,0),&(0,1),&dots,&(0,d-1),array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1398.png"
 ALT="\begin{displaymath}
\begin{array}{cccc}
(0,0), &amp; (0,1), &amp; \dots, &amp; (0, d-1),
\end{array}\end{displaymath}">|; 

$key = q/{displaymath}s=R'(z)1+qaz^{q-1}+(q+h)bz^{q+h-1}+cdots=1+()lambda^{frac{q-1}{q}}+cdots.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="508" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="\begin{displaymath}
s = R'(z)1 + qaz^{q-1} + (q + h)bz^{q+h-1} + \cdots = 1 + ()\lambda^{\frac{q-1}{q}} + \cdots .
\end{displaymath}">|; 

$key = q/{displaymath}R'(z)=1+sumfrac{A}{(z-a)^2}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img1247.png"
 ALT="\begin{displaymath}
R'(z) = 1 + \sum\frac{A}{(z-a)^2}.
\end{displaymath}">|; 

$key = q/{displaymath}A=frac{1}{R'(alpha)-1}=frac{1}{s-1}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="\begin{displaymath}
A = \frac{1}{R'(\alpha) - 1} = \frac{1}{s - 1}.
\end{displaymath}">|; 

$key = q/u_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img327.png"
 ALT="$u_1$">|; 

$key = q/a_j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img971.png"
 ALT="$a_j$">|; 

$key = q/ab;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1390.png"
 ALT="$ab$">|; 

$key = q/D_{(1)},D_{(2)},dots,D_{(p)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img728.png"
 ALT="$D_{(1)}, D_{(2)},\dots, D_{(p)}$">|; 

$key = q/displaystyleR'_p(alpha)=R'(alpha)R'(alpha_1)cdotcdotcdotR'(alpha_{p-1});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$\displaystyle R'_p(\alpha) = R'(\alpha)R'(\alpha_1)\cdot\cdot\cdot R'(\alpha_{p-1})$">|; 

$key = q/(d+1)^{mbox{{scriptsize{{'esimo}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1013.png"
 ALT="$(d + 1)^{\mbox{\scriptsize {\'esimo}}}$">|; 

$key = q/displaystyleR'(alpha_1)F_2(z),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img423.png"
 ALT="$\displaystyle R'(\alpha_1)F_2(z),$">|; 

$key = q/{displaymath}array{{rcl}X=P(A,y)Y=Q(A,y).array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img606.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
X = P(A, y) \\\\
Y = Q(A, y).
\end{array}\end{displaymath}">|; 

$key = q/{displaymath}frac{d^n-d}{2}<A,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="\begin{displaymath}
\frac{d^n - d}{2} &lt; A,
\end{displaymath}">|; 

$key = q/{displaymath}rho=B,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="32" BORDER="0"
 SRC="|."$dir".q|img241.png"
 ALT="\begin{displaymath}
\rho = B,
\end{displaymath}">|; 

$key = q/F'(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img561.png"
 ALT="$F'(z)$">|; 

$key = q/z^{2p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img748.png"
 ALT="$z^{2p}$">|; 

$key = q/{displaymath}array{{rcl}z_1&=&z+a+psi(z),z_2&=&z_1+a+psi(z_1),&vdots&z_n&=&z_{n-1}+a+psi(z_{n-1}),{par{array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="107" BORDER="0"
 SRC="|."$dir".q|img470.png"
 ALT="\begin{displaymath}
\begin{array}{rcl}
z_1 &amp; = &amp; z + a + \psi(z), \\\\
z_2 &amp; = &amp; ...
...\
z_n &amp; = &amp; z_{n-1} + a + \psi(z_{n-1}), \\\\
\par\end{array}
\end{displaymath}">|; 

$key = q/z';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$z'$">|; 

$key = q/R'(alpha)>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img958.png"
 ALT="$R'(\alpha) &gt;1$">|; 

$key = q/{calL}(midzmid);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img552.png"
 ALT="${\cal L}(\mid z\mid )$">|; 

$key = q/{displaymath}midPhi'(t)mid>C>1hspace{0.2in}{mbox{para}}hspace{0.2in}midtmid=1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1075.png"
 ALT="\begin{displaymath}
\mid\Phi'(t)\mid &gt; C &gt; 1 \hspace{0.2in}{\mbox{para}}\hspace{0.2in} \mid t\mid = 1.
\end{displaymath}">|; 

$key = q/+displaystylefrac{pi}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1318.png"
 ALT="$+\displaystyle\frac{\pi}{2}$">|; 

$key = q/C_{-1}^{(1)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1185.png"
 ALT="$C_{-1}^{(1)}$">|; 

$key = q/{displaymath}R(z)=A_0z^d+A_1z^{d-1}+cdots+A_{d-1}z+t=A(z)+t,hspace{0.2in}R'(z)=A'(z),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="554" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1356.png"
 ALT="\begin{displaymath}
R(z) = A_0z^d + A_1z^{d - 1} + \cdots + A_{d-1}z + t = A(z) + t, \hspace{0.2in} R'(z) = A'(z),
\end{displaymath}">|; 

$key = q/{displaymath}Z=R(z)=z+h-sumfrac{A}{z-a},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1233.png"
 ALT="\begin{displaymath}
Z = R(z) = z + h - \sum\frac{A}{z -a},
\end{displaymath}">|; 

$key = q/z_{lambda'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img874.png"
 ALT="$z_{\lambda'}$">|; 

$key = q/(alpha_1alpha_2dotsalpha_n);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1420.png"
 ALT="$(\alpha_1\alpha_2\dots\alpha_n)$">|; 

$key = q/{displaymath}midsmid;=;mids'mid;<1.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1000.png"
 ALT="\begin{displaymath}
\mid s\mid \; = \;\mid s'\mid \; &lt; 1.
\end{displaymath}">|; 

$key = q/{displaymath}R_n(z,lambda)=z{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="\begin{displaymath}
R_n(z, \lambda) = z \end{displaymath}">|; 

$key = q/{displaymath}midA_0mid(rho-M)^d-midA_1mid(rho-M)^{d-1}-cdots-[midA_{d-1}+1mid](rho-M)-rho>0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img1366.png"
 ALT="\begin{displaymath}
\mid A_0\mid (\rho - M)^d - \mid A_1\mid (\rho - M)^{d-1} - \cdots - [\mid A_{d-1} + 1\mid ](\rho - M) - \rho &gt; 0
\end{displaymath}">|; 

$key = q/D_infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1219.png"
 ALT="$D_\infty$">|; 

$key = q/-{Large{frac{1}{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="$-\Large\frac{1}{2}$">|; 

$key = q/R_p(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img790.png"
 ALT="$R_p(z)$">|; 

$key = q/D_1,D_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img899.png"
 ALT="$D_1, D_3$">|; 

$key = q/R_{-1}^{(0)}(z),R_{-1}^{(1)}(z),dots,R_{-1}^{(d-1)}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1391.png"
 ALT="$R_{-1}^{(0)}(z), R_{-1}^{(1)}(z), \dots, R_{-1}^{(d-1)}(z)$">|; 

$key = q/R_{q-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img234.png"
 ALT="$R_{q-1}$">|; 

$key = q/R_n(z)=R_{n'}(z');MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$R_n(z)=R_{n'}(z')$">|; 

$key = q/{displaymath}array{{ccc}mid{R(z)-alpha}mid&<&kmid{z-alpha}mid,mid{R_n(z)-alpha}mid&<&k^nmid{z-alpha}mid.array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="261" HEIGHT="53" BORDER="0"
 SRC="|."$dir".q|img353.png"
 ALT="\begin{displaymath}\begin{array}{ccc}
\mid {R(z) - \alpha}\mid &amp; &lt; &amp; k\mid {z-\...
..._n(z) - \alpha}\mid &amp; &lt; &amp;k^n\mid {z-\alpha}\mid .
\end{array}\end{displaymath}">|; 

$key = q/a-mu<0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img478.png"
 ALT="$a - \mu &lt; 0$">|; 

$key = q/displaystylefrac{1}{midzmid^{h-1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img582.png"
 ALT="$\displaystyle\frac{1}{\mid z\mid ^{h-1}}$">|; 

$key = q/Z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img861.png"
 ALT="$Z = 0$">|; 

$key = q/midsmid>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$\mid s \mid &gt; 1$">|; 

$key = q/3^k;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="20" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1195.png"
 ALT="$3^k$">|; 

$key = q/C_{-(n+1)};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1208.png"
 ALT="$C_{-(n+1)}$">|; 

$key = q/{displaymath}S_k(a_{-n})=a_{-(n-k)}hspace{1.0in}(k=1,2,...,n).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="385" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="\begin{displaymath}
S_k(a_{-n}) = a_{-(n-k)} \hspace{1.0in} (k = 1, 2, ..., n).
\end{displaymath}">|; 

$key = q/m=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1289.png"
 ALT="$m = 2$">|; 

$key = q/Delta';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img588.png"
 ALT="$\Delta'$">|; 

$key = q/sneq-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$s\neq-1$">|; 

$key = q/bb_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1439.png"
 ALT="$bb_1$">|; 

$key = q/midzmid<midz_nmid;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img549.png"
 ALT="$\mid z\mid &lt; \mid z_n\mid $">|; 

$key = q/a=R_q(a);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="$a = R_q(a)$">|; 

$key = q/{z'}_{-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1180.png"
 ALT="${z'}_{-1}$">|; 

$key = q/{Large{{frac{1}{s-1}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\Large {\frac{1}{s-1}}$">|; 

$key = q/a_n;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img577.png"
 ALT="$a_n$">|; 

$key = q/pmalpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img451.png"
 ALT="$\pm \alpha$">|; 

$key = q/C_{-n'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1343.png"
 ALT="$C_{-n'}$">|; 

$key = q/D^0,D^1,dots,D^{p'-1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img807.png"
 ALT="$D^0, D^1, \dots, D^{p' - 1}$">|; 

$key = q/z=infty;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img240.png"
 ALT="$z = \infty$">|; 

$key = q/R_{q-1}(z)=frac{A}{(z-rho)^k}+overline{omega};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img250.png"
 ALT="$R_{q-1}(z) = \frac{A}{(z-\rho)^k} + \overline{\omega}$">|; 

$key = q/R'(zeta)=0,c=R(zeta);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1303.png"
 ALT="$R'(\zeta) = 0, c = R(\zeta)$">|; 

$key = q/D_0,D_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img897.png"
 ALT="$D_0, D_2$">|; 

$key = q/z^{p+2},z^{p+3},dots,z^{2p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img696.png"
 ALT="$z^{p+2}, z^{p+3}, \dots, z^{2p}$">|; 

$key = q/Z=z+o({calL}midzmid);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img607.png"
 ALT="$Z = z + o({\cal L}\mid z\mid )$">|; 

$key = q/n=p-1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img811.png"
 ALT="$n = p-1$">|; 

$key = q/<1-a;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1086.png"
 ALT="$&lt; 1 - a$">|; 

1;

