Definition:Gamma Function/Hankel Form

From ProofWiki
Jump to navigation Jump to search

Definition

The Hankel 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


Source of Name

This entry was named for Hermann Hankel.


Sources