Reciprocal of gamma function

This article is about a particular entire function: a holomorphic function defined on the whole of $\mathbb {C}$
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Definition

As the reciprocal of the gamma function

It is defined as:

$z\mapsto {\frac {1}{\Gamma (z)}}$

if $z$ is not a simple pole of the gamma function. If $z$ is a simple pole, it sends $z$ to the residue at $z$.