Residue of Gamma Function

Theorem
Let $\Gamma$ be the Definition:Gamma Function.

Let $n$ be a non-negative integer.

Then:


 * $\displaystyle \Res \Gamma {-n} = \frac {\paren {-1}^n} {n!}$

Proof
By Poles of Gamma Function, $\Gamma$ has simple poles at the non-positive integers, so $-n$ is a simple pole of $\Gamma$.

Then: