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
- 1864: Hermann Hankel: Die Euler'schen Integrale bei unbeschränkter Variabilität des Argumentes (Z. Math. Phys. Vol. 9: pp. 1 – 21)
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.5$: Permutations and Factorials: $(17)$