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Gamma function

{title2=$\operatorname*{Res}_{z=-n}\Gamma(z)=\frac{(-1)^n}{n!}$}

The <Gamma function recurrence> and $\Gamma(z)\sim1/z$ at zero imply a <simple pole> at every $z=-n$, $n\geq0$, with <residue> $(-1)^n/n!$.

Gamma function residue at a nonpositive integer

Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 46 / 4 / Solution

Gamma function residue at a nonpositive integer ( $Res_{z = - n} Γ (z) = \frac{( - 1 ) ^{n}}{n !}$ )

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Gamma function residue at a nonpositive integer (Resz=−n​Γ(z)=n!(−1)n​)

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Gamma function residue at a nonpositive integer ( $Res_{z = - n} Γ (z) = \frac{( - 1 ) ^{n}}{n !}$ )

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