meromorphic

Dr. Joshi used the vivid image of volcanoes dotting a landscape to describe meromorphic functions.

It says that you can basically recreate a meromorphic function if you know the locations of the poles and the behavior, or to use Dr. Joshi’s word, strength of the function around the poles.

A function which has no singular points for finite values of z other than poles is called a meromorphic function.

Thus, for example, the hyperelliptic surface discussed by Humbert, 329 of which the co-ordinates are meromorphic functions of two variables of the simplest kind, with four sets of periods, is characterized by pg = 1, pa = −1; or again, any surface possessing a linear system of curves of which the order exceeds twice the deficiency of the individual curves diminished by two, is reducible by birational transformation to a ruled surface or is a rational surface.

The single valued functions which occur, as explained above, in the inversion of algebraic integrals of the first kind, for p > 1, are meromorphic.