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### Meromorphic Functions

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Date: 09/18/98 at 12:33:37
From: Duke Desabrais
Subject: Modular Forms

What is a meromorphic function?
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Date: 09/18/98 at 12:57:29
From: Doctor Nick
Subject: Re: Modular Forms

Hi Duke -

I don't know what your background is so I have to guess a bit. A
meromorphic function is a complex function that is analytic everywhere
except for possibly a discrete subset of its domain, that is, except
at some, possibly infinitely many, points. At these points, the
function goes to infinity in a polynomial way. Another way of saying
this is that the function is analytic, except for some non-essential
isolated singularies.

As plainly as I can say it: a meromorphic function is one that is
really nice, except at some isolated points where it doesn't behave

Here is the definition given by the CRC Concise Encyclopedia of
Mathematics:

A meromorphic function is complex analytic in all but a discrete
subset of its domain, and at those singularities it must go to
infinity like a polynomial (i.e., have no essential singularities).
An equivalent definition of a meromorphic function is a complex
analytic map to the Riemann Sphere.

- Doctor Nick, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Functions
High School Imaginary/Complex Numbers

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