From: ullrich@math.okstate.edu
Newsgroups: sci.math
Subject: Re: meromorphic functions
Date: Wed, 06 Jan 1999 19:04:52 GMT
Keywords: What are meromorphic functions?

In article <76vrhb$mip$1@inf6serv.rug.ac.be>,
  fmeissch@eduserv2.rug.ac.be (Frank Meisschaert) wrote:
> What is the (exact) definition of meromorphic functions?
>
> Frank Meisschaert

       Do you have two books on complex analysis that differ on
the exact definition? Never mind, I actually know of a fairly new
book on complex analysis by a couple of big names where the
definition is very inexact. So:

        First note this is the exact definition in one variable.
Suppose that V is an open subset of the plane. Roughly, a function
is meromorphic in V if it's holomorphic (ie analytic) in V except
for poles.
        Precisely: f is meromorphic in V if there exists a
set P contained in V (P may be empty) such that P has no limit
points in V (limit points on the boundary of V are allowed),
such that f is a function from V\P to C, f is holomorphic in
V\P, and |f| tends to infinity at any point of P. (The points
of P are the "poles" of f.)

        There are a lot of other equivalent formulations.

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