Definition:Gamma Function/Hankel Form

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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 $\C$.


Also known as

Some authors refer to the gamma function as Euler's gamma function, after Leonhard Paul Euler.

Some French sources call it the Eulerian function.


Also see


Source of Name

This entry was named for Hermann Hankel.


Sources