Reciprocal of gamma function: Difference between revisions
(New page: {{particular entire function}} ==Definition== ===As the reciprocal of the gamma function=== It is defined as: <math>z \mapsto \frac{1}{\Gamma(z)}</math> if <math>z</math> is ''not'' a...) |
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<math>z \mapsto \frac{1}{\Gamma(z)}</math> | <math>z \mapsto \frac{1}{\Gamma(z)}</math> | ||
if <math>z</math> is ''not'' a simple pole of the gamma function. If <math>z</math> is a simple pole, it sends <math>z</math> to the | if <math>z</math> is ''not'' a simple pole of the gamma function. If <math>z</math> is a simple pole, it sends <math>z</math> to 0. | ||
===In terms of Hankel's loop contour=== | |||
Let <math>\gamma</math> denote [[Hankel's loop contour]]. The reciprocal of the gamma function is then defined as: | |||
<math>z \mapsto \int_\gamma e^{-w} w^{-z} \, dw</math> | |||
Latest revision as of 19:17, 18 May 2008
This article is about a particular entire function: a holomorphic function defined on the whole of
View a complete list of entire functions
Definition
As the reciprocal of the gamma function
It is defined as:
if is not a simple pole of the gamma function. If is a simple pole, it sends to 0.
In terms of Hankel's loop contour
Let denote Hankel's loop contour. The reciprocal of the gamma function is then defined as:
