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Meromorphic Functions

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

What is a meromorphic function?

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 
too badly.

Here is the definition given by the CRC Concise Encyclopedia of 

   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
Associated Topics:
High School Functions
High School Imaginary/Complex Numbers

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