Definition:Gamma Function/Hankel Form

Definition
The  form of the Gamma function is:
 * $\displaystyle \frac 1 {\Gamma \left({z}\right)} = \dfrac 1 {2 \pi i}z \oint \frac {e^t \, \mathrm d t} {t^z}$

where the contour starts at $-\infty$, circles the origin in an anticlockwise direction, and returns to $-\infty$.

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

Also see

 * Equivalence of Definitions of Gamma Function