Residues of the Gamma function
= Residues of the Gamma function
{title2=$\operatorname{Res}_{s=-j}\Gamma(s)=(-1)^j/j!$}
The <Gamma function recurrence> gives $\Gamma(s)=\Gamma(s+j+1)/(s(s+1)\cdots(s+j))$. Its numerator equals one at $s=-j$, so the <residue> there is $(-1)^j/j!$ for every nonnegative integer $j$.