# Definition:Gamma Function/Hankel Form

## Definition

The Hankel form of the gamma function is:

$\ds \frac 1 {\map \Gamma z} = \dfrac 1 {2 \pi i} \oint_\HH \frac {e^t \rd t} {t^z}$

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

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

## Source of Name

This entry was named for Hermann Hankel.