Definition:Gamma Function/Hankel Form

Definition
The  form of the Gamma function is:


 * $\displaystyle \frac 1 {\Gamma \left({z}\right)} = \dfrac 1 {2 \pi i} \oint_{\mathcal H} \frac {e^t \, \mathrm d t} {t^z}$

where $\mathcal H$ is the contour starting at $-\infty$, circling the origin in an anticlockwise direction, and returning to $-\infty$.

The Hankel form is valid for all $\C$.

Also see

 * Equivalence of Definitions of Gamma Function