This function is Weierstrass's ,
traditionally written with a gothic p, on which he founded the theory of elliptic functions. However,
and from there on,
*S*'_{k}(*z*) = -*kS*_{k+1}(*z*). Looking in the other direction, integrals of
exist, although they are no longer represented by Eisenstein series, and not necessarily periodic nor single valued because of the different paths that could be taken by contour integrals defining them.

Nevertheless, there are traditional names and symbols associated with the first two integrals, according to which

= | (193) | ||

= | (194) |