Meromorphic function

In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a set of isolated points, which are poles of the function.[1] The term comes from the Greek meros (μέρος), meaning "part".[a]

Every meromorphic function on D can be expressed as the ratio between two holomorphic functions (with the denominator not constant 0) defined on D: any pole must coincide with a zero of the denominator.

The gamma function is meromorphic in the whole complex plane.
  1. ^ Hazewinkel, Michiel, ed. (2001) [1994]. "Meromorphic function". Encyclopedia of Mathematics. Springer Science+Business Media B.V.; Kluwer Academic Publishers. ISBN 978-1-55608-010-4.


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