Meromorphic FunctionsDate: 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 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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