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\usepackage{graphicx}
\topmargin 0in \textheight 575pt
\evensidemargin 0.4in \oddsidemargin 0.2in
\textwidth 420pt \marginparwidth 0in \marginparsep 0pt

\hyphenation{su-pon-ga-mos}\hyphenation{co-rres-pon-di-en-tes}\hyphenation{ge-ne-ral}\hyphenation{ha-bien-do}\hyphenation{po-si-ti-va}\hyphenation{cir-cun-fe-ren-cia}\hyphenation{si-tua-dos}\hyphenation{e-xis-tie-ra}\hyphenation{in-va-rian-tes}\hyphenation{}\hyphenation{}\hyphenation{}\hyphenation{}\hyphenation{}\hyphenation{me-dian-te}\hyphenation{re-fe-ren-tes}\hyphenation{re-fe-ren-cia}


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\lthtmldisplayA{displaymath892}%
\begin{displaymath}
\alpha = R_{p+k-h}(\alpha) = R_q(\alpha).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1234}%
$h > k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1236}%
$q = p + k - h < p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1238}%
$q \geq 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1244}%
$\alpha, \alpha_1, \alpha_2, ...$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1252}%
$R_p(z) = z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1254}%
$Z = R_p(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12651}%
$\displaystyle R'_p(\alpha) = R'(\alpha)R'(\alpha_1)\cdot\cdot\cdot R'(\alpha_{p-1})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12653}%
$\displaystyle R'_p(\alpha_1)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12655}%
$\displaystyle R'_p(\alpha_2) ;$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12657}%
$\textstyle \vdots$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1260}%
$R_n(z) = z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath893}%
\begin{displaymath}
R(z) = \alpha + s(z - \alpha) + a(z - \alpha)^q + \cdots  \hspace{0.25in}(a \neq 0).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12666}%
$\displaystyle R_n(z)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12668}%
$\displaystyle \alpha$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12669}%
$\displaystyle + s^n(z-\alpha)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12670}%
$\displaystyle + as^{n-1}[ 1 + s^{q-1} + s^{2(q-1)} + \cdots$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12671}%
$\displaystyle + s^{(n-1)(q-1)} ](z - \alpha)^q + \cdots$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12673}%
$\displaystyle R_n(z) - z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12675}%
$\displaystyle (s^n - 1)(z - \alpha)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12676}%
$\displaystyle + as^{n-1}[1 + s^{q-1} + s^{2(q-1)} + \cdots
+ s^{(n-1)(q-1)}](z - \alpha)^q + \cdots$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1274}%
$R(z) - z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1276}%
$R_n(z) - z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1278}%
$s = +1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12683}%
$\displaystyle R(z) - z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12685}%
$\displaystyle a(z - \alpha)^q + \cdots,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12688}%
$\displaystyle na(z - \alpha)^q + \cdots,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1286}%
$s^r = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1288}%
$r>1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1292}%
$r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1306}%
$s^{q-1} = +1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1308}%
$q-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1322}%
$\Large {e^{2i\pi\frac{m}{r}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1328}%
$d^n -d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1330}%
$\Large\frac{d^n - d}{n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1346}%
$t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath894}%
\begin{displaymath}
n\sum{\frac{1}{t-1}} + \sum\frac{1}{s^n - 1} + 1 = 0,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1364}%
$n = 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath895}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1368}%
$\pm1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1374}%
$2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath896}%
\begin{displaymath}
\sum\frac{1}{s-1} + 1 = 0.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath897}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1390}%
$t\neq+1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1392}%
$s\neq-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1404}%
$\mid t\mid  \leq1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1412}%
$s'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12762}%
$\displaystyle 4\sum^{\frac{d^2 + d}{3}}_{1}\Re\left(\frac{1}{t-1}\right) + \sum_{1}\Re\left(\frac{1}{-s-1}\right) + \Re\left(\frac{1}{-s' -1}\right) + 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12764}%
$\displaystyle 0,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12765}%
$\displaystyle 4\sum^{\frac{d^2-d}{2}}_{1}\left(-\frac{1}{2} -P\right) + \sum^{d}_{1}\left(-\frac{1}{2} - Q\right) + \Re\left(\frac{1}{-s' - 1}\right) + 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1416}%
$P$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1418}%
$Q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1420}%
$d \geq 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1422}%
$\frac{d^2 - d}{2} \geq 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12773}%
$\displaystyle \Re\left(\frac{1}{-s' - 1}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12775}%
$\displaystyle -1 + 4\sum^{\frac{d^2 - d}{2}}_{1}\frac{1}{2} + \sum^{d}_{1}\frac{1}{2} + H,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12778}%
$\displaystyle 2 + K,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12780}%
$\displaystyle \sum^{d}_{1}\left(\frac{1}{s-1}\right) + \frac{1}{s' - 1} + 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12783}%
$\displaystyle \sum^{d}_{1}\left(-\frac{1}{2} - L\right) + \Re\left(\frac{1}{s' - 1}\right) + 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12785}%
$\displaystyle 0 \hspace{0.1in} (L \geq 0),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12786}%
$\displaystyle \Re\left(\frac{1}{s' - 1}\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12788}%
$\displaystyle -1 + \sum^{d}_{1}\left(-\frac{1}{2}\right) + \Sigma{L},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12791}%
$\displaystyle M \geq 0.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12794}%
$\textstyle \geq$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12798}%
$\displaystyle 2 > 0.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1424}%
$s' = u + iv$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath898}%
\begin{displaymath}
u-1 \geq 0
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath899}%
\begin{displaymath}
u+1 < 0,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath900}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1434}%
$\mid t \mid$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath901}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath902}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1460}%
$\Large\frac{1}{s^n - 1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1462}%
$-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1466}%
$\mid s \mid > 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1468}%
$\mid s \mid < 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1470}%
$-\Large\frac{1}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath903}%
\begin{displaymath}
-A < \sum^{d + 1}_{1}\Re\left(\frac{1}{s^n - 1}\right) + 1 < + A,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1476}%
$A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath904}%
\begin{displaymath}
n\sum^{\frac{d^n - d}{n}}_{1}\Re\left(\frac{1}{t-1}\right) < - \left(\frac{d^n - d}{2}\right)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath905}%
\begin{displaymath}
\frac{d^n - d}{2} < A,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1482}%
$\Large\frac{d^n - d}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12845}%
$\displaystyle n\sum^{\frac{d^n - d}{n}}_{1}\frac{1}{t-1} + \sum^{d + 1}_{1}\frac{1}{s^n - 1} + 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12848}%
$\displaystyle \sum^{d + 1}_{1}\frac{1}{s-1} + 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath906}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath907}%
\begin{displaymath}
\beta_{n}(s) = \frac{1}{s^n - 1} - \frac{1}{n}\frac{1}{s-1}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1498}%
$\beta_n(s)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1500}%
$s = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1502}%
$-\Large\frac{n-1}{2n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath908}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1512}%
$\Re[\beta_n(s)]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1528}%
$\mid t \mid > 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1530}%
$t = +1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1540}%
$z= 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1542}%
$q > 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath909}%
\begin{displaymath}
R(z) = z + az^q + bz^{q+h} + \cdots
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1546}%
$R(z) + \lambda$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1548}%
$\lambda$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1552}%
$R_n(z, \lambda)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath910}%
\begin{displaymath}
R_n(z, \lambda) = z \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath911}%
\begin{displaymath}R(z)+ \lambda = z
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1560}%
$\lambda = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath912}%
\begin{displaymath} \frac{\partial}{\partial z}[R_n(z, \lambda) - z] \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath913}%
\begin{displaymath}\frac{\partial}{\partial z}[R_n(z) + \lambda - z] \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath914}%
\begin{displaymath}
\frac{\partial}{\partial z}R_n(z, \lambda)\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath915}%
\begin{displaymath} \frac{\partial}{\partial z}[R(z) + \lambda] = R'(z),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1588}%
$R(z) + \lambda = z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath916}%
\begin{displaymath}
\lambda + az^q + bz^{q+h} + \cdots = 0
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1592}%
$\Large\lambda^{\frac{1}{q}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath917}%
\begin{displaymath}
z = A\lambda^{\frac{1}{q}} + B\lambda^{\frac{2}{q}} + \cdots
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath918}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath919}%
\begin{displaymath}
q + q' + q'' + \cdots,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1604}%
$q, q', q''$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1612}%
$a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1622}%
$p + q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12929}%
$\textstyle R_{p+q}(a_{-p+q})  =  a,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12930}%
$\displaystyle R_{p+q}(a_{-p})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay12931}%
$\textstyle = R_q[R_p(a_{-p})] = R_q(a).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1624}%
$a_{-p} = a_{-p-q}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1626}%
$a = R_q(a)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1630}%
$[z \mid S(z)]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath920}%
\begin{displaymath}
S(z) = R_q(z).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath921}%
\begin{displaymath}
a, a_{-1}, a_{-2}, \dots, a_{-n}, \dots,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath922}%
\begin{displaymath}
S(a_{-n}) = a_{-(n-1)},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath923}%
\begin{displaymath}
S_k(a_{-n}) = a_{-(n-k)} \hspace{1.0in} (k = 1, 2, ..., n). 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath924}%
\begin{displaymath}
a_{-p} = a_{-p-q} \hspace{0.5in} (q\geq1),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath925}%
\begin{displaymath}
S_{p+q-1}(a_{-p}) = S_{p+q-1}(a_{-p-q}).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath926}%
\begin{displaymath}
S_{p+q-1}(a_{-p}) = S_{q-1}[S_p(a_{-p})] = S_{q-1}(a) = a,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath927}%
\begin{displaymath} S_{p+q-1}(a_{-p-q}) = a_{-1}. \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath928}%
\begin{displaymath}
a = a_{-1}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1642}%
$S(z) = \infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1644}%
$S(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1648}%
$R_q(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1652}%
$\overline{\omega}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath929}%
\begin{displaymath}
R[R_{q-1}(z)] = S(z) = \mbox{ polinomio  en }\hspace{0.2cm} z,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath930}%
\begin{displaymath}
R_{q-1}(z) = \overline{\omega}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath931}%
\begin{displaymath}
S(z) = \infty \hspace{0.5in}{\mbox y}\hspace{0.5in} z = \infty.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1656}%
$\Large\frac{1}{R_{q-1}(z) - \overline{\omega}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1660}%
$P(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath932}%
\begin{displaymath}
R_{q-1}(z) = \overline{\omega} + \frac{1}{P(z)}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1662}%
$(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1664}%
$\overline{\omega}'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath933}%
\begin{displaymath}
R_{q-1}(z) = \overline{\omega} + \frac{1}{P(z)} = \overline{\omega}' + \frac{1}{P'(z)}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1666}%
$P'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath934}%
\begin{displaymath}
\overline{\omega} - \overline{\omega}' = \frac{P(z) - P'(z)}{P(z)P'(z)}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1672}%
$\overline{\omega} = \overline{\omega}'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath935}%
\begin{displaymath}
R(z) = \frac{A}{(z - \overline{\omega})^h} + B,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1678}%
$B$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1686}%
$Z = R(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1688}%
$Z = R_{q-1}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1690}%
$R_{q-1}(z) = \overline{\omega} + \Large\frac{1}{P(z)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1692}%
$R_{q-1}(\infty) = \overline{\omega}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath936}%
\begin{displaymath}
R_{q-1}[R(z)] = S(z) = \mbox{ polinomio  en }\hspace{0.2cm} z.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1696}%
$R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1698}%
$R_{q-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1700}%
$R_{q-1}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1702}%
$\rho$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath937}%
\begin{displaymath}
R(z) = \rho + \frac{1}{Q(z)},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1704}%
$Q(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath938}%
\begin{displaymath}
\rho + \frac{1}{Q(z)} = \frac{A}{(z - \overline{\omega})^h} + B,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1708}%
$z = \infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath939}%
\begin{displaymath}
\rho  = B,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1712}%
$(z-\overline{\omega})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath940}%
\begin{displaymath}
A = \mbox{const}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath941}%
\begin{displaymath}
R(z) = \frac{A}{(z-\overline{\omega})^h} + \rho.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1718}%
$C$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1720}%
$D$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath942}%
\begin{displaymath}
R_{q-1}(z) = \frac{C}{(z - \rho)^k} + D,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1726}%
$z- \rho$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath943}%
\begin{displaymath}
\frac{C}{(z - \rho)^k} + D = \overline{\omega} + \frac{1}{P(z)}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1738}%
$R_{q-1}(z)  =  \frac{A}{(z-\rho)^k} + \overline{\omega}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13017}%
$\displaystyle R(z)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13019}%
$\displaystyle \frac{A}{(z-\overline{\omega})^h} + \rho,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13020}%
$\displaystyle R_{q-1}(z)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13022}%
$\displaystyle \frac{C}{(z-\rho)^k} + \overline{\omega},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath944}%
\begin{displaymath}
R_{q-1}[R(z)] = R[R_{q-1}(z)]
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath945}%
\begin{displaymath}
\frac{A}{C^h}(z - \rho)^{kh} + \rho = \frac{C}{A^k}(z - \overline{\omega})^{kh} + \overline{\omega}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1744}%
$z^{kh}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1746}%
$z^{kh - 1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1748}%
$k = h = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13031}%
$\displaystyle \frac{A}{C^h}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13033}%
$\displaystyle \frac{C}{A^k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13034}%
$\displaystyle \overline{\omega}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13036}%
$\displaystyle \rho.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath946}%
\begin{displaymath}
R(z) = \frac{A}{(z - \overline{\omega})^h} + \overline{\omega}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath947}%
\begin{displaymath}
R(z) - \overline{\omega} = \frac{A}{(z-\overline{\omega})^h}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1754}%
$z = \overline{\omega}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1760}%
$1\circ$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1762}%
$2\circ$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1764}%
$Z = Az^m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1766}%
$0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1768}%
$\infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1770}%
$3\circ$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1772}%
$Z = \Large\frac{A}{z^m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1780}%
$n-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1782}%
$R_{-1}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1784}%
$c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1790}%
$R(z) = c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1794}%
$c'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath948}%
\begin{displaymath}
R_n(z) = R_{n-1}[R(z)] = c'
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13064}%
$\displaystyle R_{n-1}(x)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13066}%
$\displaystyle c',$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13069}%
$\displaystyle x.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1796}%
$x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath949}%
\begin{displaymath}
c' = R_{n-1}(c).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1804}%
$R_{-(n-1)}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1814}%
$c, R(c), ..., R_{n-2}(c), R_{n-1}(c)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1816}%
$n=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1832}%
$D_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1848}%
$R(\varepsilon)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1852}%
$\varepsilon$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1866}%
$R^{(D)}_{-1}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1870}%
$b$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1872}%
$b'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath950}%
\begin{displaymath}
R(b) = R(b') = a ;
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1882}%
$L$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1892}%
$L_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1904}%
$R^{D}_{-1}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1928}%
$z_{-1} = R_{-1}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1930}%
$z_{-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1938}%
$\gamma$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1956}%
$\gamma^n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath951}%
\begin{displaymath}
R^{(D)}_{-(n+n')}(z) = R^{(D)}_{ -n}[R^{(D)}_{-n'}(z)],
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1958}%
$R^{(D)}_{-n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1960}%
$R^{(D)}_{-n'}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1964}%
$\gamma^{n'}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1976}%
$R^{(D)}_{-n}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1984}%
$d - 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2002}%
$\epsilon$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2016}%
$1-\epsilon$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2032}%
$\epsilon_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2042}%
$\epsilon_{-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2048}%
$R(z) = a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2082}%
$R(z) - a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2084}%
$2\gamma\pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2094}%
$\gamma \geq 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2100}%
$\gamma = d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2108}%
$\Delta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2122}%
$u_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2124}%
$u_k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2126}%
$ik$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2128}%
$L_1, ..., L_p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2132}%
$T = (i_1, k_1)(i_2, k_2)...(i_p, k_p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2134}%
$T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath952}%
\begin{displaymath}
T = (1,2)^{\lambda_1}(2,3)^{\lambda_2}...(d-1, d)^{\lambda_{d-1}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2136}%
$\lambda_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2138}%
$\lambda_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2142}%
$u_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2152}%
$\lambda_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2158}%
$u_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2170}%
$\lambda_3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2174}%
$u_3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2190}%
$\gamma, \gamma', \gamma'', ...$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2192}%
$(\gamma - 1)+(\gamma' - 1)+(\gamma'' - 1)+ \cdots -$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2200}%
$2(d-1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2208}%
$D_1, D_2, ...$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2210}%
$D = D_p,
D_1 = D_{p+1}, ...$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2212}%
$D, D_1, ..., D_{p-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2220}%
$D_{p-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2234}%
$D_{p-h}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2238}%
$n (mod p)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2246}%
$D_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2248}%
$n = 4, p = 3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2252}%
$R_{-4}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2254}%
$c, R_3(c), R(c'') {\mbox y} R_2(c')$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2256}%
$c, c', c''$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2262}%
$D, D_1, D_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2276}%
$[ z \mid R_p(z)]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2278}%
$^\circ 3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
{\newpage\clearpage
\lthtmlinlineA{tex2html_nomath_inline6268}%
\oe%
\lthtmlinlineZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3916}%
\begin{displaymath}
R(z) = \alpha + s(z-\alpha) + ()(z-\alpha)^2 + \cdots \hspace{0.25in} 
(\mid s\mid\ < 1).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4224}%
$\rho > 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4232}%
$\mid {z-\alpha}\mid\ \leq\rho$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3917}%
\begin{displaymath}\begin{array}{ccc}
\mid {R(z) - \alpha}\mid\  & < & k\mid {z-\alpha}\mid\ ,\\
\mid {R_n(z) - \alpha}\mid\  & < &k^n\mid {z-\alpha}\mid\ .
\end{array}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4248}%
$s \neq 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4250}%
$\displaystyle\frac{R_n(z) - \alpha}{s^n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4252}%
$F(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3918}%
\begin{displaymath}
F[R(z)] = sF(z)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4256}%
$F(\alpha) = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4258}%
$F'(\alpha) = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4260}%
$ t = F(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4262}%
$z = \alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4266}%
$t_1 = st$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3919}%
\begin{displaymath}
t_n = F[R_n(z)] = s^nt.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4268}%
$t_n = s^{\pm n}t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4270}%
$t = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4272}%
$G (n \geq 1) $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3920}%
\begin{displaymath}
z_1 = z^q + az^{q+r} + \cdots = R(z) \hspace{0.25in} (q>1),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4278}%
$[R_n(z)]^{\frac{1}{q^n}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13361}%
$\displaystyle u_n =$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13362}%
$\textstyle [R_n(z)]^{\frac{1}{q^n}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13363}%
$\displaystyle =  z_n^{\frac{1}{q^n}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13364}%
$\displaystyle u_{n+1} =$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13365}%
$\textstyle [R_{n+1}(z)]^{\frac{1}{q^{n+1}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13366}%
$\displaystyle =  [R^{\frac{1}{q}}(z_n)]^{\frac{1}{q^n}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3921}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4284}%
$H(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3922}%
\begin{displaymath}
\frac{1}{z}R^{\frac{1}{q}}(z) = 1 + lz + \cdots .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3923}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4286}%
$[H(z_n)]^{\frac{1}{q^n}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4288}%
$\frac{1}{q^n}\log\,[H(z_n)]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4290}%
$z_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4296}%
$H(z_n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3924}%
\begin{displaymath}
\mid {H(z_n) - 1}\mid\  < \frac{1}{2}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3925}%
\begin{displaymath}
\mid {H(z_n) - 1}\mid\  < A\mid {z_n}\mid  \hspace{0.25in}(A, \mbox{   constante positiva}).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4300}%
$\mid {w}\mid\  < \frac{1}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3926}%
\begin{displaymath}
\mid {\log (1 + w)}\mid\  < \mid w\mid  + \mid w\mid ^2 + \mid w\mid ^3 + \cdots < 2\mid w\mid ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3927}%
\begin{displaymath}
\mid {\log H(z_n)}\mid\  < 2A\mid {z_n}\mid .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4302}%
$\sum\displaystyle\frac{2A}{q_n}\mid {z_n}\mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4304}%
$\mid {z_n}\mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4306}%
$[R_n(z)]^{\textstyle\frac{1}{q^n}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4312}%
$\Phi(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3928}%
\begin{displaymath}
\begin{array}{rcl}
& \Phi[R(z)] \hspace{1.0cm}  =  \hspace{1.0cm} \lim_{n=\infty}{\left [R(z) {n+1} \right]}^\frac{1}{q^n}, & 
\end{array} \\
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3929}%
\begin{displaymath}
\begin{array}{rcl}
\Phi^q(z) = & \lim_{n = \infty}\left\{\left[R(z) {n+1} \right]^{\frac{1}{q^{n+1}}}\right\}^q = &
\lim_{n=\infty}{ \left[R(z) {n+1} \right] }^\frac{1}{q^n}, 
\end{array} 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3930}%
\begin{displaymath}
\begin{array}{rcl}
& \Phi[R(z)] \hspace{1.0cm}  =  \hspace{1.0cm} \lim_{n=\infty}{\left [R(z)_{n+1} \right]}^\frac{1}{q^n}, & 
\end{array} \\
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3931}%
\begin{displaymath}
\begin{array}{rcl}
\Phi^q(z) = & \lim_{n = \infty}\left\{\left[R(z)_{n+1} \right]^{\frac{1}{q^{n+1}}}\right\}^q = &
\lim_{n=\infty}{ \left[R(z)_{n+1} \right] }^\frac{1}{q^n}, 
\end{array} 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3932}%
\begin{displaymath}
\Phi[R(z)] = \Phi^q(z).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4316}%
\begin{displaymath}
\begin{array}{ll}
F(f(z)) = \lambda F(z) & \hspace{2.0cm} \mbox{ecuaci\'on de Schr\"oder} \\
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4320}%
$t = \Phi(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4328}%
$t_1 = t^q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4336}%
$te^{\textstyle\frac{2i\phi N}{q^n}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4338}%
$N$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4348}%
$n^o \; 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4364}%
$t = s^\lambda t_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4368}%
$t_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4372}%
$s=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4378}%
$\displaystyle
\frac{N\pi}{q-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3933}%
\begin{displaymath}
\rho = e^{\textstyle c(\omega + \frac{2N\pi}{q-1})},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4384}%
$0, 1, 2, \dots, q-2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4396}%
$(\alpha, \alpha_1, \dots, \alpha_{p-1})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4398}%
$\delta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4402}%
$\delta_1, \delta_2, \dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4404}%
$\alpha_1, \alpha_2, \dots\,$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4408}%
$\delta, \delta_p, \delta_{2p}, \dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4410}%
$\delta_1, \delta_{p+1}, \delta_{2p+1}\dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4412}%
$\delta_h, \delta_{p+h}, \delta_{2p+h}, \dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4414}%
$\delta_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4416}%
$\displaystyle\frac{1}{n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4420}%
$\delta, \delta_1, \dots, \delta_{p-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4426}%
$\alpha, \alpha_1, \dots, \alpha_{p-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13459}%
$\displaystyle F[R(z)]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13461}%
$\displaystyle R'(\alpha)F_1(z),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13462}%
$\displaystyle F_1[R(z)]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13464}%
$\displaystyle R'(\alpha_1)F_2(z),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13465}%
$\displaystyle F_2[R(z)]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13467}%
$\displaystyle R'(\alpha_2)F_3(z),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13469}%
$\displaystyle F_{p-1}[R(z)]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay13471}%
$\displaystyle R'(\alpha_{p-1})F_p(z),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3934}%
\begin{displaymath}
F[R_p(z)] = sF(z) \hspace{0.35in} [s = R'(\alpha)R'(\alpha_1) \dots R'(\alpha_{p-1})].
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4434}%
$\alpha, \alpha_1, \dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3935}%
\begin{displaymath}
z_1 = R(z) = z + \frac{1}{2}R''(\alpha)(z-\alpha)^2 + \cdots
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4442}%
$R''(\alpha)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3936}%
\begin{displaymath}
z_1 = z + a + \frac{b}{z} + \cdots \hspace{0.3in}(a\neq0).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3937}%
\begin{displaymath}
z_1 = z + a + \psi(z),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4448}%
$\psi(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3938}%
\begin{displaymath}
\mid \psi(z)\mid\  < \frac{C}{\mid z\mid ^\gamma} \hspace{0.3in} (C, \gamma: \mbox{  constantes   positivas})
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4452}%
$\Gamma$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4454}%
$O$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4460}%
$z = -r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4466}%
$\mu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4472}%
$\mu < a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4476}%
$z+a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4484}%
${\cal D}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4486}%
$z_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4488}%
$z + 2a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4490}%
$2\mu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4494}%
$z + na$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4496}%
$n\mu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4502}%
$Ox$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4506}%
$\mu / a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap13520}%
\includegraphics[scale=0.35]{fig/imagev1}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4518}%
$\pm \alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4522}%
$BT$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4524}%
$B'T'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4534}%
$BAB'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3939}%
\begin{displaymath}
\mu < \frac{C}{\rho\gamma}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4546}%
$(r, +\infty)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4550}%
$\mid \psi(z)\mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4552}%
$\omega$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3940}%
\begin{displaymath}
\sin \omega = \frac{C}{a} \frac{1}{\rho^\gamma}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4556}%
$x \sin\omega + y \cos\omega = \rho$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4558}%
$\rho+$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4560}%
$\displaystyle\frac{d^2\rho}{d\omega^2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3941}%
\begin{displaymath}
\gamma\rho \left[ 1 + (\gamma + 1)\frac{\cos^2\omega}{\sin^2\omega}\right],
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4570}%
$ML$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4572}%
$M'L'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4574}%
$MB$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4576}%
$M'B'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap13563}%
\includegraphics[scale = 3.4]{fig/image2}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4600}%
$\psi(z), \psi(z_1), \psi(z_2), \dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3942}%
\begin{displaymath}
\begin{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\end{array} 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3943}%
\begin{displaymath}
z_n = z + na + \sum_0^{n-1}\psi(z_i), 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3944}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4606}%
$\psi(z_i)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4608}%
$+\mu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4610}%
$-\mu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4614}%
$x > -A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3945}%
\begin{displaymath}
x_n > n(a - \mu) - A
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4620}%
$a - \mu < 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4622}%
$x_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4624}%
$\mid z_n\mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4630}%
$\mid z_n\mid\  > (a - \mu\varepsilon)n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4632}%
$\varepsilon > 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4634}%
$\displaystyle\frac{\mid 1\mid }{z_n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4636}%
$ < $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4638}%
$\displaystyle\frac{B}{n+1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3947}%
\begin{displaymath}
z_n = z + na + \theta\sum_1^n\frac{C'B\gamma}{n\gamma} \hspace{0.3in}(\mid \theta\mid\  < 1)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3948}%
\begin{displaymath}
z_n = z + na + H_n\sum_1^n\frac{1}{n\gamma},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4646}%
$H_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4648}%
$0 < \gamma < 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3949}%
\begin{displaymath}
z_n = z + na + \theta_nn^{1-\gamma}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4650}%
$\theta_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3950}%
\begin{displaymath}
z_n = na + \Lambda_nn^{1-\gamma}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4654}%
$\Lambda_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4658}%
$na$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4662}%
$\gamma = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4664}%
$n^{1-\gamma}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4666}%
${\cal L}n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3951}%
\begin{displaymath}
\psi(z) = \frac{b}{z} + \chi(z), \hspace{0.3in}  \mid \chi(z)\mid\  < \frac{k}{\mid z\mid ^{1+\beta}} \hspace{0.3in} (k, \beta > 0).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3952}%
\begin{displaymath}
\begin{array}{rcl}
z_n & = & an + \frac{b}{a}{\cal L}n + u_n,  \\
z_{n+1} & = & an + a + \frac{b}{a}{\cal L}(n+1) + u_{n+1}.
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4674}%
$z_{n+1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3953}%
\begin{displaymath}
z_{n+1} = z_n + a + \frac{b}{z_n} + \chi(z_n),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3954}%
\begin{displaymath}
u_{n+1} - u_n = \frac{b}{a}\left[ \frac{1}{n} - {\cal L}\left(1 + \frac{1}{n}\right)  \right] + b\left(\frac{1}{z_n} - \frac{1}{an}\right) + \chi(z_n).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3955}%
\begin{displaymath}
\frac{1}{n} - {\cal L}\left(1+\frac{1}{n}\right) = \frac{1}{2n^2} - \frac{1}{3n^3} + \cdots = \frac{\lambda_n}{2n^2}(\lim \lambda_n = 1)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3956}%
\begin{displaymath}
-\frac{b(z_n - na)}{naz_n},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3957}%
\begin{displaymath}
\begin{array}{rcl}
\mid z_n\mid  & > & Kn \\
\mid z_n - a\mid  & < & K'{\cal L}n;
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4678}%
$K$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4680}%
$K'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4686}%
$\displaystyle\frac{{\cal L}n}{n^2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3958}%
\begin{displaymath}
\mid \chi(z_n)\mid\  < \frac{K}{\mid z_n\mid ^{1+\beta}} < \frac{K'}{n^{1+\beta}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3959}%
\begin{displaymath}
u_n = u_1 + \sum_1^{n-1}(u_{i+1} - u_i),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4688}%
$u_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3960}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3961}%
\begin{displaymath}
z_n = a(n-1) + \frac{b}{a}{\cal L}(n-1) + F(z_1) + \varepsilon_{n-1}(z_1).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3962}%
\begin{displaymath}
F(z_1) = F[R(z)] = F(z) + a
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3963}%
\begin{displaymath}
R_n(z) - na - \frac{b}{a}{\cal L}n;
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4726}%
$n^0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4734}%
$x > A \;(A > r)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3964}%
\begin{displaymath}
F(z) = z + o({\cal L}\mid z\mid ),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4736}%
$o({\cal L}\mid z\mid )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4738}%
${\cal L}\mid z\mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3965}%
\begin{displaymath}
F(z) = \lim_{n=\infty}\left[ z_n - \frac{b}{a}{\cal L}n - na \right].
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3966}%
\begin{displaymath}
z_n = z + na + \sum_0^{n-1}\frac{b}{z_i} + \sum_0^{n-1}\chi(z_i),
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{\newpage\clearpage
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\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}%
\lthtmldisplayZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4740}%
$\sum\chi(z_i)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4744}%
$\displaystyle\frac{b}{a}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4750}%
$\sum_1^n\frac{1}{i}$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath3968}%
\begin{displaymath}
G(z) = \sum_1^\infty\left( \frac{1}{z_n} - \frac{1}{na} \right)
\end{displaymath}%
\lthtmldisplayZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4754}%
$1/z$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4760}%
$\mid z_{n+1}\mid > \mid z_n\mid $%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4764}%
$\mid z_1\mid\  > \ \mid z\mid $%
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{\newpage\clearpage
\lthtmldisplayA{displaymath3969}%
\begin{displaymath}
\frac{\pi}{2} - \arg .z > \arcsin\frac{\mid \psi(z)\mid }{a} \hspace{0.3in} [\psi = z_1 - z - a]
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{\newpage\clearpage
\lthtmldisplayA{displaymath3970}%
\begin{displaymath}
\frac{x}{\mid z\mid } > \frac{\mid \psi(z)\mid }{a}.
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\lthtmldisplayZ
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{\newpage\clearpage
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$\mid \psi(z)\mid\  <$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4768}%
$\displaystyle\frac{C}{\mid z\mid }$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4770}%
$x >$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$\displaystyle\frac{C}{a}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4774}%
$A >$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3971}%
\begin{displaymath}
G(z) = \sum_1^\infty\frac{na-z_n}{naz_n}.
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{\newpage\clearpage
\lthtmldisplayA{displaymath3972}%
\begin{displaymath}
z_n = z + na + \Theta_n{\cal L}n,
\end{displaymath}%
\lthtmldisplayZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4782}%
$\Theta_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4788}%
$G(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3973}%
\begin{displaymath}
G(z) = \sum_1^{\infty}\frac{-z}{naz_n} + \sum_1^{\infty}\frac{- \Theta_n {\cal L}n}{naz_n}.
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4790}%
$\mid \Theta_n\mid\  < \Theta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4792}%
$\mid z_n\mid\  > Kn$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4796}%
$\frac{\Theta}{aK}\sum_1^\infty \displaystyle\frac{{\cal L}n}{n^2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3974}%
\begin{displaymath}
\sum_1^\infty\frac{z}{naz_n} = \sum_1^N + \sum_{N+1}^\infty,
\end{displaymath}%
\lthtmldisplayZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4800}%
$\mid z\mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4802}%
$\sum_1^N\displaystyle\frac{1}{na}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4804}%
$\mid z\mid\  < \mid\ z_n\mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4806}%
$\sum_1^N\displaystyle\frac{1}{n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4808}%
${\cal L}N$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4810}%
${\cal L}(\mid z\mid )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3975}%
\begin{displaymath}
\frac{\mid z\mid }{aK}\sum_{N+1}^\infty\frac{1}{n^2} < \frac{\mid z\mid }{NaK},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4812}%
$\displaystyle\frac{\mid z\mid }{N}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3976}%
\begin{displaymath}
\mid G(z)\mid\  < C'{\cal L}\mid z\mid ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4816}%
$C'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3977}%
\begin{displaymath}
F(z) = z + o({\cal L}\mid z\mid ).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4818}%
$b=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3978}%
\begin{displaymath}
F(z) = z + \mbox{func. acotada}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4824}%
$(x > A)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4826}%
$F'(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3979}%
\begin{displaymath}
R(z) = z + a + \frac{b}{z} + \frac{c}{z^p} + \frac{d}{z^q} + \cdots,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$p, q, \dots$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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\begin{displaymath}
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$\frac{1}{z^h}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4842}%
$R'(z) - 1$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$\displaystyle\frac{C}{\mid z\mid ^h}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$\displaystyle\frac{C'}{\mid z\mid ^h}$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath3981}%
\begin{displaymath}
1 - \frac{C'}{\mid z\mid ^h} < \mid\  R'(z)\mid\  < 1 + \frac{C}{\mid z\mid ^h}.
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3982}%
\begin{displaymath}
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3983}%
\begin{displaymath}
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\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$\mid F'(z)\mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3984}%
\begin{displaymath}
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\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3985}%
\begin{displaymath}
\frac{1}{\mid z\mid ^h} + \frac{1}{\mid z_1\mid ^h} + \cdots + \frac{1}{\mid z_n\mid ^h} + \cdots
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4874}%
$\Large\frac{1}{\mid z\mid }$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3986}%
\begin{displaymath}
\begin{array}{rcl}
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\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4876}%
$a_n$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3987}%
\begin{displaymath}
\sum_0^\infty = \sum_0^N + \sum_{N+1}^\infty,ø
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4886}%
$\displaystyle\frac{N + 1}{\mid z\mid ^h}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4888}%
$\mid z_n\mid\  <\ \mid\ z\mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4892}%
$\displaystyle\frac{N + 1}{\mid z\mid }$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4896}%
$\displaystyle\frac{1}{\mid z\mid ^{h-1}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4898}%
$\mid z_n\mid\  > K_n$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4900}%
$h > 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4902}%
$\Large\frac{1}{N}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4904}%
$F'(z) = 1 + o(\frac{1}{z})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4914}%
$\left(A > \frac{C}{a} \right)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4924}%
$\Delta'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3988}%
\begin{displaymath}
\begin{array}{rcl}
F[R(z)] & = & F(z) + a, \\
F'[R(z)] & = & \frac{1}{R'(z)} F'(z)
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4932}%
${\cal L}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4934}%
${\cal L}_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3989}%
\begin{displaymath}
F(z_1) = z_1 + o({\cal L}\mid z_1\mid ),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3990}%
\begin{displaymath}
F(z) = F(z_1) - a = z_1 + o({\cal L}\mid z_1\mid ),
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4936}%
$z + o({\cal L}\mid z\mid )$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4942}%
$\Delta(x > A)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4948}%
$\Delta: 1^0 R_n(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4950}%
$2^0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4954}%
$3^0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4962}%
$+\infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4964}%
$Z = F(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4968}%
$Z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4970}%
${\cal E}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4972}%
$x = A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4976}%
$X$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3991}%
\begin{displaymath}
Z = F(z) = P(x, y) + iQ(x, y).
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3992}%
\begin{displaymath}
\begin{array}{rcl}
X = P(A, y)\ \\
Y = Q(A, y).
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\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$Z = z + o({\cal L}\mid z\mid )$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4982}%
$Y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4984}%
$y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4990}%
$-\infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3993}%
\begin{displaymath}
Y_1 = Q(A, y_1) = Q(A, y_2) \hspace{0.3in} (y_1 < y_2)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline4998}%
$y_3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5000}%
$y_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5002}%
$y_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3994}%
\begin{displaymath}
\frac{\partial Q}{\partial y}(A, y_3) = 0 = \frac{\partial P}{\partial x}(A, y_3),
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5004}%
$\displaystyle\frac{\partial P}{\partial x}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3995}%
\begin{displaymath}
\frac{dY}{dX} = \displaystyle\frac{\frac{\partial Q}{\partial y}(A, y)}{\frac{\partial P}{\partial y}(A, y)} = \displaystyle\frac{-\frac{\partial P}{\partial x}(A, y)}{\ \ \frac{\partial P}{\partial x}(A, y)},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5034}%
$Q(x, y) = $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3996}%
\begin{displaymath}
\frac{dy}{dx} = \displaystyle\frac{-\frac{\partial Q}{\partial x}}{\ \  \frac{\partial Q}{\partial y}} = \displaystyle\frac{-\frac{\partial Q}{\partial x}}{\ \ \frac{\partial P}{\partial x}};
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5040}%
$\displaystyle\frac{dy}{dx}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5044}%
$Z + na$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5064}%
$(Z \mid  Z + na)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5068}%
$z = G(Z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5074}%
$\Delta_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3997}%
\begin{displaymath}
F[R(z)] = F(z) + a,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3998}%
\begin{displaymath}
\begin{array}{rcl}
R(z) & = & G(Z + a), \\
R_n(z) & = & G(Z + na).
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3999}%
\begin{displaymath}
R_n[R_{n'}(z)] = R_{n + n'}(z),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4000}%
\begin{displaymath}
z + n'a + na \hspace{0.3in}\mbox{ y } \hspace{0.3in} Z + (n + n')a,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5090}%
$R''(\alpha) \neq 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5092}%
$\alpha = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4001}%
\begin{displaymath}
z_1 = R(z) = z - az^2 + bz^3 + \cdots,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5096}%
$\left( z = \frac{1}{t}, z_1 = \frac{1}{t_1} \right)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4002}%
\begin{displaymath}
t_1 = t + a + \frac{a^2 - b}{t} + \cdots.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4003}%
\begin{displaymath}
z_{-1} = z + az^2 + \cdots ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5120}%
$D'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap13914}%
\includegraphics[scale = 3]{fig/image3}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5134}%
$\displaystyle\frac{\pi}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4004}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4005}%
\begin{displaymath}
F[R(z)] = F(z) + a.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4006}%
\begin{displaymath}
F(z) = \frac{1}{z} + o\left(\log  \mid\frac{1}{z}\mid\right).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4007}%
\begin{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) \neq 0.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4008}%
\begin{displaymath}
z_1 = z - az^{p+1} + \cdots .
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5172}%
$\displaystyle\frac{1}{z}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5174}%
$\displaystyle\frac{1}{z_1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4009}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4010}%
\begin{displaymath}
\begin{array}{rcl}
z & = & t^{\frac{1}{p}}, \\
z_1 & = & t_1^{\frac{1}{p}},
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4011}%
\begin{displaymath}
\begin{array}{rcccl}
t_1^{\frac{1}{p}} & = & t^\frac{1}{p}\left( 1 + \frac{a}{t} + \frac{b}{t^{1+\frac{1}{p}}} + \cdots \right), & \\
t_1 & = & t\left( 1 + \frac{a}{t} + \frac{b}{t^{1 + \frac{1}{p}}} + \cdots \right)^p & = & t\left( 1 + \frac{pa}{t} + \frac{pb}{t^{1 + \frac{1}{p}}}  + \cdots \right), \\
t_1 & = & t + pa + \frac{pb}{t^\frac{1}{p}} + \cdots & = & S(t).
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5176}%
$S(t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5178}%
$t^{\frac{1}{p}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5184}%
$-\pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5186}%
$+\pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5196}%
$\displaystyle\frac{2\pi}{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5198}%
$\displaystyle\frac{\pi}{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5200}%
$\displaystyle\frac{3\pi}{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4012}%
\begin{displaymath}
t_1 = S(t)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5204}%
$t_1 = [R(z)]^p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5210}%
$t_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5214}%
$t_1^\frac{1}{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5220}%
$t^\frac{1}{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4013}%
\begin{displaymath}
t_1^\frac{1}{p} = \omega R(z) = \omega z_1,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5226}%
$\omega = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5240}%
$t^\frac{1}{p} = z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5242}%
$\frac{2\pi}{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5254}%
$\omega = +1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5256}%
$t_1^\frac{1}{p} = z_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4014}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5262}%
$t^\frac{1}{p}, t_1^\frac{1}{p},\dots,t_n^\frac{1}{p},\dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5264}%
$\left( \displaystyle\frac{\pi}{p}, \frac{3\pi}{p} \right)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4015}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5266}%
$z, z_1, z_2, \dots, z_n, \dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5270}%
$t_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5274}%
$z_n = R_n(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5280}%
$z = \displaystyle\sqrt[p]{t}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5294}%
$\left( \frac{\pi}{p} \right)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4016}%
\begin{displaymath}
z_{-1} = R_{-1}(z) = z + az^{p+1} + \cdots,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5308}%
$\frac{\pi}{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5318}%
$\displaystyle\frac{p}{2\pi}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5320}%
$2p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4017}%
\begin{displaymath}
z_n = \frac{1}{\sqrt[\textstyle p]{n\,p\,a + o(n^{1-\frac{1}{p}})}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap14035}%
\includegraphics[scale = 4]{fig/image4}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5332}%
$D, \Delta, D', \Delta'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5334}%
$p = 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5336}%
$1^0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5344}%
$(t^p = z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4018}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4019}%
\begin{displaymath}
\begin{array}{rcccl}
w & = & P(z) & = & z + \lambda_2z^2 + \cdots + \lambda_pz^p, \\
w_1 & = & P(z_1). & &
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5354}%
$\omega_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4020}%
\begin{displaymath}
w_1 = w + A_{p+1}w^{p+1} +A_{p+2}w^{p+2} + \cdots,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5370}%
$A_{p+2} = A_{p+3} = \cdots = A_{2p} = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4021}%
\begin{displaymath}
w_1 = w + A_{p+1}w^{p+1} +A_{2p+1}w^{2p+1} + \cdots,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4022}%
\begin{displaymath}
\begin{array}{rcl}
R(z) + \lambda_2R^2(z) + \cdots + \lambda_pR^p(z) & = & z + \lambda_2z^2 + \cdots + \lambda_pz^p \\
& & + A_{p+1}(z + \lambda_2z^2 + \cdots + \lambda_pz^p)^{p+1} \\
& & + A_{2p+1}(z +  \cdots )^{2p+1} + \cdots.
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5374}%
$z^p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5376}%
$z^{p+1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5378}%
$A_{p+1} = a_{p+1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4023}%
\begin{displaymath}
\begin{array}{l}
(z + a_{p+1}z^{p+1} + a_{p+2}z^{p+2} + \cdots + a_{2p}z^{2p} +  \cdots) \\
 + \lambda_2z^2(1 + a_{p+1}z^p + a_{p+2}z^{p+1} + \cdots + a_{2p}z^{2p-1} + \cdots)^2 \\
+ \lambda_3z^3(1 + a_{p+1}z^p + \cdots + a_{2p}z^{2p-1} + \cdots)^3 + \cdots \\
+ \lambda_pz^p(1 + a_{p+1}z^p + a_{p+2}z^{p+1} + \cdots + a_{2p}z^{2p-1} + \cdots)^p \\
= z + \lambda_2 z^2 + \cdots \\\ \ \ \ \ + \lambda_pz^p + a_{p+1}z^{p+1}(1 + \lambda_2z + \cdots + \lambda_pz^{p-1})^{p+1} + Hz^{2p+1}.
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5380}%
$z^{p+2}, z^{p+3}, \dots, z^{2p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4024}%
\begin{displaymath}
\begin{array}{rcl}
a_{p+2} + 2a_{p+1}\lambda_2 & = & (p+1)a_{p+1}\lambda_2, \\
a_{p+3} + 2\lambda_2a_{p+2} + 3a_{p+1}\lambda_3 & = & \frac{p(p+1)}{2}a_{p+1}\lambda_2^2 + (p+1)a_{p+1}\lambda_3, \\
& \vdots & \\
F_k(\lambda_2, \lambda_3, \dots, \lambda_{k-1}) + ka_{p+1}\lambda_k & = & \Phi_k(\lambda_2, \lambda_3, \dots, \lambda_{k-1}) + (p+1)a_{p+1}\lambda_k, \\
F_p(\lambda_2, \lambda_3, \dots, \lambda_{p-1}) + pa_{p+1}\lambda_p & = & \Phi_k(\lambda_2, \lambda_3, \dots, \lambda_{p-1}) + (p+1)a_{p+1}\lambda_p.
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5382}%
$F_k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5384}%
$\Phi_k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5386}%
$\lambda_2, \lambda_3, \dots, \lambda_{k-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5390}%
$a_{2p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5392}%
$a_{p+1} = a \;\; (a \neq 0)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4025}%
\begin{displaymath}
\begin{array}{rcl}
(p - 1) a\lambda_2 & = & a_{p+2}, \\
(p - 2) a\lambda_3 & = & a_{p+3} + 2\lambda_2a_{p+2} - \frac{p(p+1)}{2}a\lambda_2^2, \\
& \vdots & \\
(p - k + 1)a\lambda_k & = & \Psi_k(\lambda_2, \lambda_3, \dots, \lambda_{k-1}), \\
a\lambda_p & = & \Psi_p(\lambda_2, \lambda_3, \dots,\lambda_{p-1}). 
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5394}%
$\lambda_2, \lambda_3, \dots, \\\lambda_p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5398}%
$w = P(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5400}%
$w_1 = P(z_1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4026}%
\begin{displaymath}
w_1 = w - aw^{p+1} + A_{2p+1}w^{2p+1} + \cdots = Q(w),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5404}%
$w = t^{-\frac{1}{p}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5406}%
$w_1 = t_1^{-\frac{1}{p}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4027}%
\begin{displaymath}
t_1 = S(t) = t + pa + \frac{b}{t} + \frac{c}{t^{1 + \frac{1}{p}}} + \cdots.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5412}%
$\frac{1}{t}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5414}%
$S_n(t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4028}%
\begin{displaymath}
t_n = S_n(t)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4029}%
\begin{displaymath}
t_n = p\,a\,n + \frac{b}{pa}{\cal L}n + F(t) + \varepsilon_n,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5424}%
$\Delta[R(t) > A]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4030}%
\begin{displaymath}
F(t) = t + o[{\cal L}(t)].
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5434}%
$w$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5438}%
$D^{(1)}, D^{(2)}, \dots, D^{(p)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5440}%
$ \Delta^{(1)},\Delta^{(2)}, \dots, \Delta^{(p)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5442}%
$Q_n(w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5444}%
$R(w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5446}%
$n^{0} 11$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5456}%
$D^{(i)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5460}%
$w = $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5462}%
$\displaystyle\frac{1}{\omega t^\frac{1}{p}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5464}%
$\left( \omega = e^\frac{2ik\pi}{p}  \right) $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5466}%
$w - \lambda_2w^2 + \cdots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5474}%
$D_{(1)}, D_{(2)},\dots, D_{(p)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5476}%
$\Delta_{(1)}, \Delta_{(2)}, \dots, \Delta_{(p)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5482}%
$D_{(1)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4031}%
\begin{displaymath}
\begin{array}{c}
w_n = P(z_n), \hspace{0.3in} w = P(z), \\
\!\!w_n = t_n ^{-\frac{1}{p}}, \hspace{0.3in}\ \ \ w = t^{-\frac{1}{p}}, \\
 t_n = n\,p\,a + \frac{b}{a}\ {\cal L}n + F(t) + \varepsilon_n; 
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4032}%
\begin{displaymath}
P(z_n) = \frac{1}{\sqrt[p]{npa + \frac{b}{a} {\cal L}n + f(z) + \varepsilon_n}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4033}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5484}%
$1^{0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5488}%
$P(z_n) = w_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4034}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5492}%
$w_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5494}%
$t_n^{-\frac{1}{p}} =$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5496}%
$\displaystyle\frac{1}{\sqrt{n\,a\,p + \frac{b}{a} {\cal L}n + C(z) + \varepsilon_n}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5498}%
$p+1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5500}%
$\varepsilon_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5504}%
$\displaystyle\frac{1}{t_n^\frac{1}{p}} - \frac{1}{(t_n + \varepsilon_n)^\frac{1}{p}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5506}%
$\displaystyle\frac{\varepsilon_n}{t_n^{1 + \frac{1}{p}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5508}%
$w_n^{v+1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5510}%
$w_n^{p+2}, \dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5520}%
$b, \lambda_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5522}%
$\mu_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5526}%
$z^{2p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5530}%
$D_{(i)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5532}%
$F(t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5540}%
$Q(w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5542}%
$w^{hp+1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5546}%
$f(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5550}%
$F$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5552}%
$F\left[ \frac{1}{P^p(z)} \right] = f(z) $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5558}%
$\Delta_{(i)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4035}%
\begin{displaymath}
f(z) = \frac{1}{z} + o\left({\cal L}\frac{1}{\mid z\mid}\right).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5568}%
$R(z) = z + \frac{1}{z}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5576}%
$(x > 0)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5578}%
$(x < 0)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4036}%
\begin{displaymath}
R_n(z) = \sqrt{2n + f(z) + \varepsilon_n},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4037}%
\begin{displaymath}
f\left( z + \frac{1}{z}  \right) = f(z) + 2.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4038}%
\begin{displaymath}
R(z) = z + \frac{a}{z^{p-1}} + \frac{b}{z^p} + \cdots \hspace{0.3in} (a \mbox{  real positiva})
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5596}%
$z^p = t, z_n^p = t_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4039}%
\begin{displaymath}
\begin{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.
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5600}%
$\Psi (t) = \frac{b'}{t^\frac{1}{p}} + \cdots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5602}%
$\displaystyle\frac{pa}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5606}%
$t, t_1, \dots, t_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4040}%
\begin{displaymath}
\begin{array}{lc}
t_1 = t + pa + \theta\frac{pa}{2}, & \\
t_2 = t_1 + pa + \theta_1\frac{pa}{2}, & \\
\vdots & \mid \theta_i\mid\ \leq 1, \\
t_n = t_{n-1} + pa + \theta_{n-1}\frac{pa}{2};
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4041}%
\begin{displaymath}
t_n = t + npa + n\theta'\frac{pa}{2} \hspace{0.3in}\mid \theta'\mid\ \geq 1;
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4042}%
\begin{displaymath}
\begin{array}{l}
\Re(t_n) = \Re(t) + npa + n\theta''\frac{pa}{2} \hspace{0.3in}  \mid\theta''\mid\ \leq 1, \\
\Re(t_n) > \Re(t) + n\frac{pa}{2}. 
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5624}%
$z^p = t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5636}%
$R(z_n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5650}%
$\xi_{-n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4043}%
\begin{displaymath}
R_n(\xi_{-n}) = \xi \neq 0,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5682}%
$\S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4044}%
\begin{displaymath}
R_n(z) = z - naz^{p+1} + bz^{p+2} + \cdots.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5684}%
$M(r)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5690}%
$r < \rho$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4045}%
\begin{displaymath}
M^2(r) > r^2 + n^2\mid a \mid^2r^{2(p+1)} + \mid b \mid^2r^{2(p+2)} + \cdots.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5700}%
$R_n(0) = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5708}%
$2\pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4046}%
\begin{displaymath}
R(z) = sz - a_2z^2 + \cdots + a_hz^h + \cdots,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5710}%
$s = e^{i\alpha} = e^{2i\pi\frac{m}{p}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5712}%
$m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4047}%
\begin{displaymath}
R_n(z) = s^nz + \cdots
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4048}%
\begin{displaymath}
R_p(z) = z + A_hz^h + A_{h+1}z^{h+1} + \cdots.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5716}%
$A_h \neq 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5718}%
$A_hz^h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5722}%
$R_p(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5728}%
$pp' + 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4049}%
\begin{displaymath}
R_p[R(z)] = R[R_p(z)],
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4050}%
\begin{displaymath}
\begin{array}{l}
(sz + a_2z^2 + \cdots + a_hz^h + \cdots) 
+ A_h[sz + a_2z^2 + \cdots + a_hz^h + \cdots]^h \\
+ Hz^{h+1} \\
= s[z + A_hz^h + A_{h+1}z^{h+1} + \cdots] 
 + a_2[z + a_hz^h + \cdots]^2 + a_h[z + \cdots]^h \\
+ Kz^{h+1},
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5730}%
$H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5734}%
$z^h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4051}%
\begin{displaymath}
a_h + A_hs^h = A_hs + a_h,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4052}%
\begin{displaymath}
A_hs(s^{h-1}-1) = 0.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5736}%
$A_hs \neq 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5738}%
$s^{h-1}=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5742}%
$s^p = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5744}%
$h-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5748}%
$h = pp' + 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5754}%
$n\alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5758}%
$pp'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5764}%
$\displaystyle\frac{2\pi}{pp'}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5766}%
$p'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5772}%
$D^0, D^1, \dots, D^{p' - 1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5776}%
$R(z), R_2(z), \dots, R_{p-1}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4053}%
\begin{displaymath}
\left\{
\begin{array}{llll}
D^0 & D^1 & \dots & D^{p'-1}, \\
D^0_1 & D^1_1 & \dots & D^{p'-1}_1, \\
\dots & \dots & \dots & \dots \\
D^0_{p-1} & D^1_{p-1} & \dots & D^{p'-1}_{p-1},
\end{array}
\right.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5780}%
$\mid z' \mid \leq \rho$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5784}%
$n = p-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5802}%
$R_{np}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5818}%
$\omega + $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5820}%
$\displaystyle\frac{2n\pi}{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5836}%
$\pmod{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5838}%
$\lambda p - q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5840}%
$R_{\lambda p - q} = f_\lambda(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5844}%
$R_q[f_{\lambda p}(z)] = R_\lambda(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5856}%
$z, R(z), R_2(z), \dots,$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5858}%
$ R_{p-1}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5860}%
$z = sz =$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5862}%
$e^{\textstyle\frac{2i\pi m}{p}}z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5864}%
$z = f(z), z_1 = f(t_1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5866}%
$f(t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5870}%
$z_1 = sz$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath4054}%
\begin{displaymath}
f(t_1) = sf(t) \;\;\; \mbox{de donde} \; \;\;t_1 = F[sf(t)].
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5874}%
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{\newpage\clearpage
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$t_1 = Q(t)$%
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{\newpage\clearpage
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$Q(t)=L(2-e^t)$%
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{\newpage\clearpage
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$e^{2i\pi\frac{m}{p}}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5896}%
$[z \mid  R_q(z)]$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5906}%
$z_q$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5908}%
$p > 1$%
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{\newpage\clearpage
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$R_{pq}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5914}%
$z_{\lambda pq}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$(p'\geq 1)$%
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{\newpage\clearpage
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$e^{i\alpha}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5926}%
$\pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5928}%
$z_1 = e^{i\alpha}z$%
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{\newpage\clearpage
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{\newpage\clearpage
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$e^{i\beta}z$%
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{\newpage\clearpage
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$\beta$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5944}%
$z = f(t), z_1 = f(t_1)$%
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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$\mid z_n - \alpha\mid\  > k^n\mid z - \alpha\mid $%
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{\newpage\clearpage
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$M_n(\rho)$%
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{\newpage\clearpage
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$\mid z - \alpha\mid\  \leq \rho$%
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{\newpage\clearpage
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{\newpage\clearpage
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$[z \mid R_{-1}(z)]$%
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{\newpage\clearpage
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\begin{displaymath}
F[R_{-1}(z)] = \frac{1}{s}F(z),
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$Z = 0$%
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{\newpage\clearpage
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{\newpage\clearpage
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$E''$%
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{\newpage\clearpage
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$\mid s\mid\  \geq 1$%
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{\newpage\clearpage
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{\newpage\clearpage
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$z_\lambda$%
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{\newpage\clearpage
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$\mid z_\lambda - \alpha\mid\  < \rho$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6108}%
$z_{\lambda + \mu}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$\mid z_{\lambda + \mu} - \alpha\mid\  > \rho$%
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6120}%
$(\rho, k\rho)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6122}%
$z_{\lambda'}$%
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{\newpage\clearpage
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$\mid z_{\lambda'} - \alpha\mid\  < \rho$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6136}%
$z_{\lambda' + \mu'}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6140}%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6144}%
$\rho = $%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6146}%
$\displaystyle\frac{r}{k}, \frac{r}{k^2}, \cdots, \frac{r}{k^n}, \cdots$%
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{\newpage\clearpage
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{\newpage\clearpage
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$\alpha =$%
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{\newpage\clearpage
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$\displaystyle\frac{1 + i\sqrt{19}}{2}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6160}%
$\beta =$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6162}%
$\displaystyle\frac{1 - i\sqrt{19}}{2}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6164}%
$2\alpha$%
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{\newpage\clearpage
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$2\beta$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6170}%
$\mid z\mid\  \geq 3$%
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{\newpage\clearpage
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\begin{displaymath}
\begin{array}{l}
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{\newpage\clearpage
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6178}%
$R(z) = z^2 - \frac{5}{4}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6182}%
$z = $%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6184}%
$\displaystyle\frac{+1 \pm  \sqrt{6}}{2}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6186}%
$1 \pm \sqrt{6}$%
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{\newpage\clearpage
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{\newpage\clearpage
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{\newpage\clearpage
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$\displaystyle\frac{-1 + \sqrt{2}}{2}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6198}%
$D_0, D_2$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6204}%
$\displaystyle\frac{-1\sqrt{2}}{2}$%
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{\newpage\clearpage
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$D_1, D_3$%
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{\newpage\clearpage
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$D_0$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6212}%
$z_{4n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6216}%
$z_{4n + 1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6220}%
$z_{4n + 2}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6222}%
$D_2$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6224}%
$z_{4n + 3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6226}%
$D_3$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap14541}%
\includegraphics[scale=3]{fig/image5}%
\lthtmlpictureZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6232}%
$R(z) = z^d + a$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath4064}%
\begin{displaymath}
U_n(z) = \frac{R_n(z) - z}{R(z) - z} = z^{d^n -d} + \cdots + P_n(a) = 0.
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6238}%
$P_n(a)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6242}%
$a^{d^{n-1}-1}$%
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{\newpage\clearpage
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$\displaystyle\frac{d^n - d}{n}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6248}%
$(z, z_1, \dots. z_{n-1})$%
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{\newpage\clearpage
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\lthtmldisplayZ
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{\newpage\clearpage
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d^{nd - d}\Pi (z)^{d-1},
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6252}%
$\Pi$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$U_n(z) = 0$%
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{\newpage\clearpage
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\pm d^{dn-d}[P(a)]^{d-1}.
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6260}%
$(t) < 1$%
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\lthtmlcheckvsize\clearpage}

\stepcounter{chapter}
{\newpage\clearpage
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$I(z) \geq 0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8466}%
$z_0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8474}%
$z-z_0$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8480}%
$2q\pi\;\;(q \geq 1)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8500}%
$q\pi$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8506}%
$q \geq 2$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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{\newpage\clearpage
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$A, h, k$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay14593}%
$\displaystyle A = \lim_{z = a}R(z)(z-a),$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay14594}%
$\displaystyle k = \lim_{z = \infty}\frac{R(z)}{z}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8520}%
$z = x + iy$%
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{\newpage\clearpage
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$\displaystyle -\frac{A}{z-a} = -\frac{A(x-a)}{(x-a)^2 + y^2} + \frac{Aiy}{(x-a)^2 + y^2},$%
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{\newpage\clearpage
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$x = a,  y > 0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8528}%
$\displaystyle\frac{Ai}{y}$%
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{\newpage\clearpage
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$\displaystyle\frac{A}{y}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8532}%
$ > 0$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8534}%
$A > 0$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8536}%
$z + iy$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8540}%
$R(Z) = kiy +$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8542}%
$ky > 0$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8546}%
$Z = X + iY$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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\begin{displaymath}
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{\newpage\clearpage
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$k = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8196}%
\begin{displaymath}
\frac{-1}{Z-\alpha} = T, \hspace{0.3in} \frac{-1}{z - \alpha} = t,
\end{displaymath}%
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{\newpage\clearpage
\lthtmldisplayA{displaymath8197}%
\begin{displaymath}
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\end{displaymath}%
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{\newpage\clearpage
\lthtmldisplayA{displaymath8198}%
\begin{displaymath}
z = R(z) = h - \sum\frac{A}{z-a}
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{\newpage\clearpage
\lthtmldisplayA{displaymath8199}%
\begin{displaymath}
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\end{displaymath}%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11614}%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11616}%
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\lthtmlinlinemathA{tex2html_wrap_inline11628}%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8588}%
$(a_j, a_{j+1})$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8600}%
$(a_1, a_2), (a_2, a_3), \dots$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8602}%
$\bf 1^0$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8606}%
$\alpha, f(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8608}%
$f'(\alpha) > 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8610}%
$R'(\alpha) >1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8200}%
\begin{displaymath}
\frac{1}{s-1} + \frac{1}{s' + 1} + \sum_1^{d-1}\frac{1}{s_i - 1} + 1 = 0
\end{displaymath}%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8618}%
$\sum$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8620}%
$s_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8624}%
$\geq 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8626}%
$d-1 \geq 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8201}%
\begin{displaymath}
\Re\left( \frac{1}{s-1} \right) + \Re\left( \frac{1}{s'-1} \right) + 1 + P = 0 \hspace{0.3in} ( P > 0)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8202}%
\begin{displaymath}
2u + 1 + P = 0.
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8203}%
\begin{displaymath}
\frac{1}{s-1} = u+iv, \hspace{0.3in} \frac{1}{s'-1} = u -iv.
\end{displaymath}%
\lthtmldisplayZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8628}%
$u < -\frac{1}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8204}%
\begin{displaymath}
\mid s\mid\ \ = \ \mid s'\mid\ \ < 1.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8630}%
$\bf 2^0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8636}%
$\alpha < \alpha' <\alpha''$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8638}%
$a_j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8640}%
$a_{j+1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8644}%
$\alpha''$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8205}%
\begin{displaymath}
R'(\alpha) > 1, \hspace{0.3in} R''(\alpha'') > 1;
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8648}%
$\alpha'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8652}%
$R'(\alpha') < 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8654}%
$(a_d, +\infty)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8658}%
$R'(\alpha')<1 \;\;(\alpha < \alpha')$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8666}%
$\displaystyle\sl\frac{1}{s-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8670}%
$(d + 1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8206}%
\begin{displaymath}
\frac{1}{s-1} = -1 - {\sum}'\frac{1}{s-1} = -1-P \hspace{0.1in}(P>0),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8207}%
\begin{displaymath}
0 < s < 1.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8672}%
$\bf 3^0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8676}%
$s = R'(\alpha) = + 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8678}%
$s > 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8680}%
$\bf 4^0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8684}%
$d - 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8690}%
$R''(\alpha) = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8720}%
$-R(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8208}%
\begin{displaymath}
R(z) = - kz - h + \sum\frac{A}{z-a},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8732}%
$Z = R_2(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8734}%
$R_2(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8764}%
${R''}_2(z) = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8768}%
$R'(y) = + 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8786}%
$n > 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8792}%
$[z, R(z)]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8796}%
$ \alpha_1, \alpha_2, \dots, \alpha_{d - 1} $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8802}%
$\alpha, \alpha'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8209}%
\begin{displaymath}
\frac{1}{s -1} + \frac{1}{s' -1} + \sum_1^{d-1}\frac{1}{s_i - 1} + 1 = 0,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8210}%
\begin{displaymath}
\mid s\mid\ \; = \;\mid s'\mid\ \; < 1.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8211}%
\begin{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)}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8820}%
$\alpha_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8826}%
$R ( z ) = A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8212}%
\begin{displaymath}
\sum_1^{d -1}\frac{1}{(s_i -1)(z - \alpha_i)} + \frac{1}{z - A} + \Phi(z) = 0,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8836}%
$\displaystyle\frac{Cz + C'}{(z - a)^2 + b^2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8838}%
$b>0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8840}%
$\displaystyle\frac{1}{z - a_i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8842}%
$s_i > 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8844}%
$\displaystyle\frac{1}{z - A}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8852}%
$(\alpha_1, \alpha_2, \dots,\alpha_{d-1}, A)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8868}%
$z = \alpha = a + bi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8878}%
$Z = A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8894}%
$(d + 1)^{\mbox{\scriptsize {\'esimo}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8213}%
\begin{displaymath}
\frac{1}{s - 1} + \sum_1^d\frac{1}{s_i - 1} + 1 = 0
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8214}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8900}%
$\displaystyle\frac{1}{s_i - 0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8908}%
$(\alpha_1, \alpha_2, \dots, \alpha_d, A)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8215}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8926}%
$s>0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8216}%
\begin{displaymath}
s = R'(\alpha) = +1, \hspace{0.3in} R''(\alpha) \neq 0
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8938}%
$\S 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay14833}%
$\displaystyle \frac{1}{R(z) - z} = \frac{l}{(z - \alpha)^2} + \frac{h}{z - \alpha} + \sum^{d-1}_1 \frac{1}{s_i - 1}\frac{1}{z - \alpha_i},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay14834}%
$\displaystyle h + \sum_1^{d - 1}\frac{1}{s_i - 1} + 1 = 0.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8940}%
$l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8217}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8956}%
$\S 10$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8958}%
$R^u(\alpha)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8218}%
\begin{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
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8968}%
$s_i - 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8978}%
$\alpha_1 < \alpha < \alpha_2$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8980}%
$\alpha_1, \alpha$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8982}%
$\alpha, \alpha_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8219}%
\begin{displaymath}
R'(z) = +1, \hspace{0.3in}   R''(z) = 0,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline8996}%
$s < -1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8220}%
\begin{displaymath}
t = \frac{z - \beta}{z - \-{\bar\beta}}, \hspace{0.3in} T = \frac{Z - \beta}{Z - \bar{\beta}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9008}%
$\bar{\beta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9014}%
$T = \Phi(t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9016}%
$\Phi^{(1)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9018}%
$\Phi^{(2)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9022}%
$\Phi = \Phi^{(1)}\Phi^{(2)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9024}%
$\Phi^{(1)}(t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9028}%
$R^{(1)}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9030}%
$R^{(2)}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9034}%
$\Phi(t) = \Phi^{(1)}\Phi^{(2)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8221}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9038}%
$bi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8222}%
\begin{displaymath}
R(z) = \frac{R^{(1)}(z)R^{(2)}(z) - b^2}{R^{(1)}(z) + R^{(2)}(z)}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9042}%
$\displaystyle\frac{\Phi(t)}{t}$%
\lthtmlinlinemathZ
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$\mid t\mid\ = 1$%
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$\mid t\mid\  < 1$%
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$\Psi(t) =$%
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{\newpage\clearpage
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$\Phi^{(1)}(t) = \Psi(t)$%
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{\newpage\clearpage
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$\Phi^{(2)}(t) = t$%
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{\newpage\clearpage
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$R^{(1)}(z) = \lambda(z)$%
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{\newpage\clearpage
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$R^{(2)}(z) = z$%
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\begin{displaymath}
R(z) = \frac{z\lambda(z) - b^2}{z + \lambda(z)}.
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$\mid\ \Phi'(t)\mid $%
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\begin{displaymath}
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{\newpage\clearpage
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$R'(z)$%
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{\newpage\clearpage
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\begin{displaymath}
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$\lambda(z)$%
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$\Phi'(t)$%
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{\newpage\clearpage
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{\newpage\clearpage
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$\mid\Phi'(t)\mid\ \geq 1$%
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{\newpage\clearpage
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{\newpage\clearpage
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$1 + $%
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{\newpage\clearpage
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$\displaystyle\frac{a^2 + b^2}{A}$%
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{\newpage\clearpage
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$1 + \frac{1}{K}$%
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{\newpage\clearpage
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$\sum\displaystyle\frac{A}{b^2 + h^2}$%
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{\newpage\clearpage
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$K = 0$%
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$\mid z\mid\ = \rho$%
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{\newpage\clearpage
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$\displaystyle\frac{R(z)}{z}$%
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{\newpage\clearpage
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$\mid z\mid\ = 1$%
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{\newpage\clearpage
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{\newpage\clearpage
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$E$%
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{\newpage\clearpage
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$(1-a, 1+a)$%
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{\newpage\clearpage
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$z', z'', \dots$%
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{\newpage\clearpage
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\begin{displaymath}
\begin{array}{rcl}
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\end{array}
\end{displaymath}%
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{\newpage\clearpage
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$\mid z^{(p)}\mid$%
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{\newpage\clearpage
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$< 1 - a$%
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{\newpage\clearpage
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$R_{n_p}(z) < C^{n_p}\mid 1 - a\mid, \;\;( C < 1 )$%
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{\newpage\clearpage
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$\displaystyle\frac{1}{n_p}$%
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{\newpage\clearpage
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\mid\ \xi^{(p)}\mid\ > K > 0;
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{\newpage\clearpage
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$\rho < 1$%
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{\newpage\clearpage
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$R_1(z)$%
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{\newpage\clearpage
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$R(z) = 0$%
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{\newpage\clearpage
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$\gamma_{-1}$%
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{\newpage\clearpage
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$\gamma;\;\ \gamma_{-1}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9222}%
$v$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9236}%
$2z\pi$%
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{\newpage\clearpage
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$v \geq 1$%
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{\newpage\clearpage
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$v = d$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9270}%
$(\gamma, \Gamma)$%
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{\newpage\clearpage
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$\delta_{-1}$%
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{\newpage\clearpage
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$\delta_{-2}$%
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{\newpage\clearpage
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$\gamma_{-2}$%
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{\newpage\clearpage
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$\gamma_{-1}, \gamma_{-2}, \dots, \gamma_{-n}, \dots$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9304}%
$\frac{1}{n}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9306}%
$\delta_{-n}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9308}%
$d\sigma_{-n}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9312}%
$\delta_{-(n-1)}$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath8235}%
\begin{displaymath}
d\sigma_{-(n-1)} =\ \mid R'(z)\mid d\sigma_{-n},
\end{displaymath}%
\lthtmldisplayZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9316}%
$\sigma_{-n}$%
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{\newpage\clearpage
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$\mid R'(z)\mid\ > K > 1$%
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{\newpage\clearpage
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$\gamma_{-n}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9328}%
$n > n'$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath8236}%
\begin{displaymath}
d\sigma_{-n} < \frac{1}{K}d\sigma_{-(n-1)},
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9332}%
$\delta_{-n-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9368}%
$R( z ) = Az^d$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9396}%
$E'$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9408}%
$R_{-h}(z)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9414}%
$\sigma_{-h}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9418}%
$R_{-h}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9426}%
$\sigma_{-2h}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9432}%
$\sigma_{-3h}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9434}%
$\sigma_{-nh}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8237}%
\begin{displaymath}
\sigma_{(n-1)h} = R_h(\sigma_{-nh}),
\end{displaymath}%
\lthtmldisplayZ
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{\newpage\clearpage
\lthtmldisplayA{displaymath8238}%
\begin{displaymath}
\xi = R_h(\xi).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9450}%
$e^{\textstyle\frac{2pi\pi}{q}}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9454}%
$P(n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8239}%
\begin{displaymath}
\sum_{\delta/n}P(n) = d^n + 1,
\end{displaymath}%
\lthtmldisplayZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9458}%
$\frac{\delta}{n}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8240}%
\begin{displaymath}
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\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9468}%
$\mu(\delta)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9476}%
$\mu(1) = 1$%
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{\newpage\clearpage
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\begin{displaymath}
P(n) = \sum\mu(\delta)d^{\mbox{$\normalsize\frac{n}{\delta}$}} \equiv 0 \hspace{0.3in}(\mbox{mod }n),
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\lthtmldisplayZ
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{\newpage\clearpage
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$\displaystyle\frac{P(n)}{n}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9494}%
$\sigma, \sigma', \sigma'', \dots$%
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{\newpage\clearpage
\lthtmldisplayA{displaymath8242}%
\begin{displaymath}
\sigma, \;\; \sigma', \;\; \sigma, \;\; \sigma', \;\; \sigma'', \;\; \sigma, \;\; \sigma', \;\; \sigma'', \;\; \sigma''', \;\; \sigma, \;\; \sigma', \;\; \dots .
\end{displaymath}%
\lthtmldisplayZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9498}%
$\sigma'$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9500}%
$\sigma_{-a_1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$\sigma_{-a_2}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9512}%
$\sigma_{-a_3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9516}%
$\sigma''$%
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{\newpage\clearpage
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$\sigma_{-a_4}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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\begin{displaymath}
\begin{array}{llllllllllll}
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& & X & & & X & & & & X & \\
& \sigma_{-a_1} & \sigma_{-a_2} & \sigma_{-a_3} & \sigma_{-a_4} & \sigma_{-a_5} & \sigma_{-a_6} & \sigma_{-a_7} & \sigma_{-a_8} & \sigma_{-a_9} & \dots 
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$\sigma_{-a_n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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\begin{displaymath}
\begin{array}{llllllll}
\sigma, & \sigma_{-a_2}, & \sigma_{-a_5}, & \sigma_{-a_9}, & \dots, & \sigma_{-a_{\frac{n(n+1)}{2}- 1}}, & \dots,
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9538}%
$\sigma^{(K)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9548}%
$2\pi\displaystyle\frac{p}{q}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9550}%
$\displaystyle\frac{1}{q}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9556}%
$p < q$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9562}%
$\displaystyle\frac{1}{Nq}\;(N = 1, 2, 3, \dots)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9580}%
$Z = z^3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9584}%
$\Theta_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9588}%
$\displaystyle\frac{\Theta_0}{2\pi}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9618}%
$\Theta$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9628}%
$\alpha, \beta, \gamma, \delta, \dots $%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmldisplayA{displaymath8245}%
\begin{displaymath}
\frac{\Theta_0}{2\pi} = 0, \hspace{0.3in}(\alpha)0(\beta)00(\gamma)000(\delta)0000(\varepsilon), \dots,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9630}%
$(\alpha),(\beta),(\gamma),\cdots$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9632}%
$\alpha, \beta, \gamma, \dots$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9644}%
$E' = \Pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8246}%
\begin{displaymath}
R(z) = kz + h - \sum\frac{A}{z - a} \hspace{0.3in} (A > 0, \;k > 1),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8247}%
\begin{displaymath}
R'(z) = k + \sum\frac{A}{(z - a)^2}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8248}%
\begin{displaymath}
R'(k) > k > 1.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8249}%
\begin{displaymath}
Z = R(z) = X + iY,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8250}%
\begin{displaymath}
\left\{
\begin{array}{l}
X = kx + h - \sum\frac{A(x - a)}{(x - a)^2 + y^2} \\
Y = ky + \sum\frac{Ay}{(x - a)^2 + y^2}.
\end{array}
\right.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8251}%
\begin{displaymath}
\mid Y\mid\ > k\mid y\mid, \hspace{0.1in} \mid y_n\mid\ > k^n\mid y\mid,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9658}%
$\lim y_n= \infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9660}%
$y > y_0 > 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8252}%
\begin{displaymath}
\mid X\mid\ > k'\mid x\mid\ \hspace{0.3in}(k' > 1)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9662}%
$\mid x\mid$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9666}%
$2P$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9668}%
$2\eta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9670}%
$\eta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8253}%
\begin{displaymath}
\mid R'(z)\mid\ > k' > 1,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9674}%
$R'(z) > k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9676}%
$\cal{D}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8254}%
\begin{displaymath}
\left\{
\begin{array}{lr}
\mid X\mid\ > k'\mid x\mid  \\
& (k > 1, k' > 1), \\
\mid Y\mid\ > k\mid y\mid  
\end{array}
\right.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9678}%
${\cal{D}}_1 = R({\cal{D}})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9722}%
$C_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9734}%
${z'}_{-1} = f(z')$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9736}%
$f(z) - f(z')$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9740}%
${z'}_{-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9742}%
$C_{-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8255}%
\begin{displaymath}
f(z) - f(z') = 0.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9752}%
$z_{-1}'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9762}%
$C_{-1}^{(1)}, C_{-1}^{(2)},\dots, C_{-1}^{(d)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9766}%
$C_{-1}^{(1)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9768}%
$C_{-1}^{(2)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9770}%
$R(\xi)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9780}%
$C_{-1}^{(1)}, C_{-1}^{(2)},C_{-1}^{(3)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9782}%
$d=3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9788}%
$C_{-1}^{(3)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9798}%
$C_{-2}^{(1)}, C_{-2}^{(2)}, C_{-2}^{(3)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9804}%
$C_{-2}^{(4)}, C_{-2}^{(5)}, C_{-2}^{(6)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9812}%
$C_{-2}^{(7)}, C_{-2}^{(8)}, C_{-2}^{(9)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9816}%
$C_{-2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9826}%
$3^k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8256}%
\begin{displaymath}
C_{-k}^{(1)}C_{-k}^{(2)}\dots C_{-k}^{(3^k)}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9828}%
$3^{k-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8257}%
\begin{displaymath}
{\cal{D}}_{-n}({\cal{D}}_{-1}<{\cal{D}}_{-2}<\cdots <{\cal{D}}_{-n})
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9836}%
$C_{-n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8258}%
\begin{displaymath}
\mid R'(z)\mid\ < k' < 1.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9846}%
$C_{-(n-1)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8259}%
\begin{displaymath}
d\sigma_{-(n-1)} = d\sigma_{-n}\mid R'(z)\mid\ \hspace{0.2in} (z \mbox{  sobre  } C_{-n}),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8260}%
\begin{displaymath}
d_{-n}\sigma < \frac{1}{k'}d_{-(n-1)}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8261}%
\begin{displaymath}
l_{-n}, \frac{1}{k'}l_{-(n-1)},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8262}%
\begin{displaymath}
l_{-n} < \frac{l_0}{{k'}^n}, \hspace{0.3in} \lim_{n = \infty}l_{-n} = 0.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9858}%
$n + 1,\; n + 2,\; n + 3,\; \dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9912}%
$C_{-n}^{(i)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9914}%
$C_{-(n+1)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9918}%
${C'}_{-(n+1)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9920}%
${C''}_{-(n+1)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9930}%
$\alpha\beta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9956}%
${C''}_{-n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9994}%
$(\lambda, +\infty)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline9996}%
$(\mu, -\infty)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10000}%
$z = \lambda$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10002}%
$z < z_1 < \cdots < z_n < \cdots, \lim_{n = \infty} z_n = +\infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10004}%
$z < \mu, z > z_1 > z_2 \dots > z_n \dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8263}%
\begin{displaymath}
\lim_{n = \infty} z_n = + \infty.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10006}%
$D_\infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10008}%
$\lambda\mu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10034}%
${\cal A}_(-n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10040}%
${\cal A}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10054}%
${\cal A}_p + {\cal D}_p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10056}%
${\cal D}_p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10060}%
${\cal A}_p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10062}%
${\cal A}_p {\cal A}_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10064}%
${\cal A}_{p'}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10066}%
$p'<p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10078}%
$c_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10082}%
$c_{n+p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10084}%
$n^{\mbox{\scriptsize {\'esimo}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10108}%
$k > d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8264}%
\begin{displaymath}
Z = R(z) = z + h - \sum\frac{A}{z -a},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay15478}%
$\displaystyle X = x + h - \sum\frac{A}{(x - a)^2 + y^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay15479}%
$\displaystyle Y = y + \sum\frac{A}{(x - a)^2 + y^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8265}%
\begin{displaymath}
y_{n+1} > y_n > \dots, > y > 0,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10128}%
$y_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8266}%
\begin{displaymath}
y_{n + 1} - y_n = y_n\sum\frac{A}{(x_n - a)^2 + n^2}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10138}%
$z_p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10142}%
$y > t_0 > 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10144}%
$y < -y_0 < 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10146}%
$x \geq x_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10148}%
$x_0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8267}%
\begin{displaymath}
z_1 - z = R(z) - z = h - \sum\frac{A}{z-a} > 0 \hspace{0.2in}(z < z_1),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10200}%
$b = R(b)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10204}%
$a'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8268}%
\begin{displaymath}
R'(z) = 1 + \sum\frac{A}{(z-a)^2}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10214}%
$R'(z) > 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10218}%
$R'(z) > k > 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10224}%
$s_1, s_2, \dots, s_n, \dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10230}%
$\alpha_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10232}%
$\beta_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10234}%
$s_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10248}%
$(a', \lambda)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8269}%
\begin{displaymath}
\mbox{ longitud } s_{n+1} > k \mbox{ longitudes }s_n \hspace{0.3in} (k > 1),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10282}%
$R(\alpha) = +1,\; R''(\alpha) \neq 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8270}%
\begin{displaymath}
R'(\alpha) = +1, \hspace{0.3in} R''(\alpha) = 0.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8271}%
\begin{displaymath}
R(z) = z - \sum\frac{A}{z-a} \hspace{0.3in}(A > 0),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay15571}%
$\displaystyle X = x - \sum\frac{A(x-a)}{(x-a)^2 + y^2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay15572}%
$\displaystyle Y = y\left[ 1 + \sum\frac{A}{(x-a)^2 + y^2} \right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10302}%
$z_1 < z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10308}%
$z_1 > z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10314}%
$\mid z_{n+1}\mid\ <\ \mid z_n\mid$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10322}%
$[R'(\alpha) = +1, R''(\alpha) = 0]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8272}%
\begin{displaymath}
Z = z^2 + 5
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10332}%
$\mid z\mid\ > 4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8273}%
\begin{displaymath}
R_{-1} = \sqrt{z - 5}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10334}%
$z = 5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8274}%
\begin{displaymath}
\mid R'(z)\mid\ > k > 1.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10338}%
$k = 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10340}%
$R'(z) = 2z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10342}%
$\mid z\mid\ \leq 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10344}%
$R(z) \geq 4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10350}%
$\mid R(z)\mid\ \geq 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10352}%
$C_n$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8275}%
\begin{displaymath}
\mid R'(z)\mid\ > k > 2.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10356}%
$l_{-n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10366}%
$\alpha = -$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10368}%
$ \displaystyle\frac{1 \pm i\sqrt{19}}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10370}%
$s = 2\alpha = 1 \pm i\sqrt{19}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10380}%
$\sqrt{z - 5}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10390}%
$\beta_{-n} - \alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10398}%
$Z = R_{-n}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10404}%
$z^m + a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10406}%
$\mid a\mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10410}%
$R(z) = $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10412}%
$\displaystyle\frac{z}{z^m + 2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10414}%
$(m \geq 2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10416}%
$m = 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10418}%
$ m > 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10422}%
$z^m = -1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8276}%
\begin{displaymath}
R'(z) = \frac{2 - (m - 1)z^m}{(z^m + 2)^2},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10426}%
$m+1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10428}%
$z = (-1)^\frac{1}{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10436}%
$\mid z\mid\ < 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10438}%
$<1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10440}%
$\mid  R(z) \mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10444}%
$\mid z^m + 2\mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10450}%
$\mid  z \mid\ < r < 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10452}%
$ \mid R(z)\mid\ < k\mid z\mid\ \;(k < 1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10460}%
$ = Z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10462}%
$m-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10464}%
$R'(\zeta) = 0, c = R(\zeta)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8277}%
\begin{displaymath}
\zeta^m = \frac{2}{m - 1},\;\;\; \mid c\mid\ = \frac{1}{m}\left( \frac{m-1}{2} \right)^{1 -\frac{1}{m}} \hspace{0.2in} (\mid c\mid\ < 1).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10486}%
$\mid  c \mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10488}%
$z = \left( \displaystyle\frac{2}{m-1} \right)^\frac{1}{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10494}%
$z = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10496}%
$\mid  z \mid\ = 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8278}%
\begin{displaymath}
\mid R'(z)\mid\ > K > 1.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8279}%
\begin{displaymath}
R'(z) = -\left[ (m - 1) - \frac{2}{z^m} \right]R^2(z)z^{m-2}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10526}%
$C_{-n} (n \geq 1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10528}%
$z^m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10530}%
$+\frac{\pi}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10532}%
$+3\frac{\pi}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8280}%
\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}} < 1,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10538}%
$-\displaystyle\frac{2}{z^m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10540}%
$-\displaystyle\frac{\pi}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10542}%
$+\displaystyle\frac{\pi}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8281}%
\begin{displaymath}
\left|  (m-1) - \displaystyle\frac{2}{z^m} \right| > \sqrt{(m - 1)^2 + \frac{1}{2^{2m - 2}}}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8282}%
\begin{displaymath}
\mid R^2(z)z^{m-2}\mid\ \geq 1.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8283}%
\begin{displaymath}
R'(z) > K > m - 1,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10552}%
$\displaystyle\frac{1}{(m - 1)^2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10556}%
$mC_{-n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10558}%
$\sum{airesC_{-n}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8284}%
\begin{displaymath}
\sum\mbox{\'area}\ C_{-n} < \frac{m}{(m-1)^2}\sum\mbox{\'area}\ C_{-(n-1)},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10560}%
$\displaystyle\frac{m}{(m-1)^2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10562}%
$(m \geq 3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8285}%
\begin{displaymath}
R(z) = \frac{z^2}{z^3 + 2}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10566}%
$(\mid z\mid\ < 1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10570}%
$z^3 = $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10572}%
$\displaystyle\frac{2}{3^3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10578}%
$\mid R' ( z)\mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10582}%
$K > 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10586}%
$z^3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10590}%
$\displaystyle\frac{3\pi}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8286}%
\begin{displaymath}
\begin{array}{ccc}
R'(z) = \left( \frac{4}{z^3} - 1 \right) R^2(z), & \mid z\mid\ < \sqrt{3}, & \mid R(z)\mid\ > 1 - \varepsilon.
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8288}%
\begin{displaymath}
\mid R'(z)\mid\ > k > 1,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10606}%
$k > \sqrt{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10608}%
$R_{-1}^{(0)}, R_{-1}^{(1)}, \dots, R_{-1}^{(d-1)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10612}%
$(\alpha_1, \alpha_2, \dots, \alpha_{n?})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10618}%
$R_{-1}^{(\alpha_1)}\left[R_{-1}^{(\alpha_2)}\left[R_{-1}^{(\alpha_3)}\left[ \dots z\right]\right]\right]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10624}%
$C_{-n'}(n' > n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10626}%
$C_{-n'}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10634}%
$1, 2, 3, \dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10656}%
$(0 < t \leq 1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10670}%
$z = f(t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10672}%
$f(t +1) = f(t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10674}%
$R(z) = f(dt)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10704}%
$R(y)=z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10716}%
${\cal D}_1 = R({\cal D})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10720}%
$\mid R'(z)\mid\ > K' > 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10724}%
$(K' < K)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10734}%
$s = R'(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10742}%
$\displaystyle\frac{1}{R_n(z) - z_0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10746}%
$\displaystyle\frac{1}{\alpha - z_0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8289}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10770}%
$\mid R'(z)\mid\ \leq K\ \;(K > 1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10776}%
$M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10778}%
$\mid t\mid\ > M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10780}%
$\mid R(z)\mid\ >\  \mid z\mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8290}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10788}%
$\mid z\mid\ \geq r' > r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8291}%
\begin{displaymath}
\mid z_1\mid\ = \mid R(z)\mid\ \geq\ \mid t\mid\ - M.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10800}%
$\mid t\mid\ - M > r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10802}%
$\mid t\mid\ = \rho$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8292}%
\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 > 0
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10804}%
$\rho^d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10808}%
$L, L > M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10810}%
$\mid t\mid\ > L$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10812}%
$r'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10816}%
$\mid R'(z)\mid\ \leq K$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10818}%
$\mid R(z)\mid\ > r'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10824}%
$R'(z) = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10834}%
$K > d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10838}%
$ \displaystyle\frac{z + z^d}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10840}%
$\ (d\geq 2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10844}%
$3^{\textstyle\frac{1}{d-1}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10846}%
$\mid z_1\mid\  > K'\mid z\mid\ \; ( K' > 1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10852}%
$\mid z_1\mid\ > k\mid z\mid,\; ( k < 1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10860}%
$c = R(\zeta)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10862}%
$R'(\zeta) = $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10864}%
$\displaystyle\frac{1 + d\zeta^{d-1}}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10866}%
$ = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10874}%
$\left( \frac{1}{d}^\frac{1}{d-1} \right)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10884}%
${C'}_{-1}, {C'}_{-2}, \dots,$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10886}%
${C'}_{-n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10888}%
${C'}_{-(n-1)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10892}%
$C'_{-n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10918}%
$(C, C')$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10922}%
$ab$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10942}%
$R_{-1}^{(0)}(z), R_{-1}^{(1)}(z), \dots, R_{-1}^{(d-1)}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10954}%
$(0, 1,2, \dots, d-1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10958}%
${C'}_{-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10960}%
$j$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10962}%
$j + 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10978}%
$\delta_{-1}^{(0)}, \delta_{-1}^{(1)}, \delta_{-1}^{(2)}, \dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10982}%
$(C_{-2}, {C'}_{-2})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8293}%
\begin{displaymath}
\begin{array}{cccc}
(0,0), & (0,1), & \dots, & (0, d-1),
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8294}%
\begin{displaymath}
\begin{array}{ccccccc}
(1,0) (1,1), \dots, (1, d-1), (2,0),  \dots, (d-1, d-1),
\end{array}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10992}%
$a_{-n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10994}%
$b_{-n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline10998}%
$(\alpha_1, \alpha_2, \dots, \alpha_n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8295}%
\begin{displaymath}
R_{-1}^{(\alpha_1)}\left[ R_{-1}^{(\alpha_2)} \left[ R_{-1}^{(\alpha_3)}[\dots(z)]\right]\right].
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11008}%
$\delta_{-n'},\;(n' > n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11010}%
$\delta_{-n'}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11028}%
$(d-1)+1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11040}%
$R(z) = z^d$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8296}%
\begin{displaymath}
z_{-n} = {\displaystyle\rho}^{\textstyle\frac{1}{d^n}}{\displaystyle{e}}^{\textstyle\frac{2iN\pi}{d^n}} \hspace{0.3in} (\mbox{para }z = \rho > 0).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8297}%
\begin{displaymath}
\mid R'(z)\mid\ > K > 1
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8298}%
\begin{displaymath}
R'(z) = \frac{1 + dz^{d-1}}{2}\ \ \  \mbox{y} \ \ \ \mid z\mid\ \geq 1,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8299}%
\begin{displaymath}
\mid R'(z)\mid\ \geq \frac{d-1}{2}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11054}%
$d\geq 4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11056}%
$\mid R'(z)\mid\ \geq \frac{3}{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8300}%
\begin{displaymath}
\mid R'(z)\mid\ > K > 1,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11064}%
$d = 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11072}%
$(C_{-1}, {C'}_{-n})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11074}%
$(\alpha_1 \alpha_2 \dots \alpha_n \dots)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11078}%
$(\alpha_1), (\alpha_1 \alpha_2), \dots, (\alpha_1 \alpha_2 \dots \alpha_n),\dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8301}%
\begin{displaymath}
\left( \frac{\alpha_1}{d} + \frac{\alpha_2}{d^2} + \cdots + \frac{\alpha_n}{d^n} \right)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11088}%
$(\alpha_1\alpha_2\dots\alpha_n)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11096}%
$t'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11098}%
$\displaystyle\frac{1}{d^n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11110}%
${\delta'}_{-n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11118}%
$\displaystyle\frac{N}{d^n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11134}%
$t=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8302}%
\begin{displaymath}
z = f(t),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11160}%
$(0, 1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11162}%
$f(1) = f(0)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8303}%
\begin{displaymath}
R(z) = f(d.t),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11166}%
$t\; (0<t<1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11216}%
$(C_{-n}, {C'}_{-n})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8305}%
\begin{displaymath}
(C_{-n}, C_{-(n-1)})\ \ \ \mbox{\'o}\ \ \ ({C'}_{-n}, {C'}_{-(n-1)}).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11232}%
$C_{-1}'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11242}%
$apqb$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11244}%
$(C, C_{-1}), (C_{-1}, {C'}_{-1}), ({C'}_{-1}, C')$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11254}%
$a_{-1} b''_{-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11256}%
$(C_{-1}, {C'}_{-1})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11258}%
$aa_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11260}%
$bb_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11262}%
$(C, C_{-1})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11264}%
$(C', {C'}_{-1})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11268}%
$a_{-1}abb_{-1}, R_{-1}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11270}%
$a_{-2}a_{-1}b_{-1}b_{-2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8306}%
\begin{displaymath} \begin{array}{cc}
R(a_{-2}) = a_{-1}, & R(b_{-2}) = b_{-1};
\end{array}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11276}%
$a_{-3}a_{-2}b_{-2}b_{-3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8307}%
\begin{displaymath}
a_{-n}a_{-(n-1)}b_{-(n-1)}b_{-n},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8308}%
\begin{displaymath}\begin{array}{cc}
R(a_{-n}) = a_{-(n-1)} & R(b_{-n}) = b_{-(n-1)}.
\end{array}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11280}%
$(a_{-i}, a_{-(i+1)})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8309}%
\begin{displaymath}
\mbox{longitud }(a_{-n}, a_{-(n-1)}) < \frac{A}{K^n},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8310}%
\begin{displaymath}
\mid a_{-n} - a_{-(n-1)}\mid\ < \frac{A}{K^n}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11284}%
$\sum\mid a_{-n} - a_{-(n-1)}\mid $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8311}%
\begin{displaymath}\begin{array}{lcr}
& \lim a_{-n} = \omega, & \\
R(\omega) = \omega, & & \mid R'(\omega)\mid\ > 1.
\end{array}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11286}%
$a_{-n} b_{-n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11288}%
$a_{-(n-1)}a_{-n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11294}%
$aa_{-1}, a_{-1} a_{-2},\dots,
a_{-n}a_{-(n+1)}, \dots, bb_{-1},b_{-1}b_{-2}, \dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11298}%
$(C_{-(n-1)},$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11300}%
$C_{-n})({C'}_{-(n-1)}, {C'}_{-n})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11304}%
$R'(\omega)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11308}%
$O'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8312}%
\begin{displaymath}
z = f(z) \hspace{0.2in} (0 \leq t \leq 1)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8313}%
\begin{displaymath}
[f(t)] = f[d.t]  \mbox{        ($d$, grado de $R$)}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11330}%
$w = \sqrt{z},\; w$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11346}%
$W = \sqrt{Z}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11348}%
$W$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11356}%
$W(w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11358}%
$W = \sqrt{R(w^2)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11362}%
$R(w^2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11366}%
$w^2 = a^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11372}%
$a^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay16162}%
$\displaystyle R(w^2) = (w^2 - a^2)^{2q+1}P(w^2) \hspace{0.3in} [P(a^2) \neq 0],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay16163}%
$\displaystyle W = \sqrt{R(w^2)} = (w - a)^{q+\frac{1}{2}}H(w),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11376}%
$H(w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11378}%
$w=a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11384}%
$(w-a)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11404}%
$w = \pm a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11414}%
$\sqrt{R(w^2)}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8314}%
\begin{displaymath}
W = R_1(w),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11416}%
$R_1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8315}%
\begin{displaymath}
W = kw + h - \sum\frac{A}{w-a},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11426}%
$\sqrt{Z}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay16196}%
$\displaystyle k\sqrt{z} + h - \sum\frac{A}{\sqrt{z} - a}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay16197}%
$\displaystyle -k\sqrt{z} + h + \sum\frac{A}{\sqrt{z} - a}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8316}%
\begin{displaymath}
2h + \sum\frac{A}{\sqrt{z} + a} - \sum\frac{A}{\sqrt{z} - a} = 0
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8317}%
\begin{displaymath}
h - \sum\frac{Aa}{z - a^2} = 0.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11440}%
$\displaystyle\frac{A}{w - a}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11442}%
$\displaystyle\frac{A'}{w + a}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11444}%
$\displaystyle\frac{(A' - A)a}{z - a^2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11446}%
$a \neq 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11448}%
$A=A'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11450}%
$h=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11452}%
$R_1(w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8318}%
\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}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11454}%
$A, a, k$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8319}%
\begin{displaymath}
Z = z\left[ k - \sum\frac{2A}{z - a^2}, \right]^2 = R(z).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11458}%
$w = \pm \sqrt{z}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11462}%
$w_1 = R_1(w),\dots, w_n = R_1(w_{n-1}), \dots$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11470}%
$z_n = w_n^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11476}%
$\alpha^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11504}%
$-c^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11506}%
$\alpha = ci$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8320}%
\begin{displaymath}
0 < k < 1, \hspace{0.3in} k + \sum\frac{2A}{a^2} > 1.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11516}%
$pq$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8321}%
\begin{displaymath}\begin{array}{lll}
\mbox{(I)                   } & R(p)=p, &  R(q)=q, \\
\mbox{(II)                  } & R(p)=p, &  R(q)=p, \\
\mbox{(III)                 } & R(p)=q, &  R(q)=q, \\
\mbox{(IV)                 } & R(p)=q, &  R(q)=p. \\
\end{array}\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11564}%
$(-1, +1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8322}%
\begin{displaymath}
w = \sqrt{\frac{1-z}{1 + z}},\hspace{0.3in} W = \sqrt{\frac{1-Z}{1 + Z}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11568}%
$W = R_1(w)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11574}%
$w = \pm i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8323}%
\begin{displaymath}
\frac{w-i}{w+i} = t \hspace{0.3in} \frac{W-i}{W+i} = T,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11580}%
$T = P(t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11582}%
$P(t)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11584}%
$(\mid t\mid\ \leq 1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8324}%
\begin{displaymath}
P(t) = e^{ia}t^m \;\;\;\;\;\; \mbox{      $a$\  real, $m$\  entero  $> 0$}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath8325}%
\begin{displaymath}
t = i\varphi, \hspace{0.3in} T = e^{i(m\varphi + a)} = e^{i\varphi},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay16285}%
$\displaystyle w = \tan\frac{\varphi}{2},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay16286}%
$\textstyle W = \tan\frac{\Phi}{2},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay16287}%
$\displaystyle z = \frac{1-w^2}{1 + w^2} = \cos\varphi,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay16288}%
$\textstyle Z = \cos\Phi = \cos(m\varphi + a).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11592}%
$\cos(m\varphi + a)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11594}%
$\cos\varphi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11600}%
$\pm \cos m\pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline11602}%
$\cos\varphi = z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}


\end{document}
