Difference between revisions of "Reciprocal gamma"

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The reciprocal gamma function is the function $\dfrac{1}{\Gamma(z)}$, where $\Gamma$ denotes the [[gamma function]].
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The reciprocal gamma function $\dfrac{1}{\Gamma}$ is defined by
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$$\left( \dfrac{1}{\Gamma} \right)(z) =\dfrac{1}{\Gamma(z)},$$
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where $\Gamma$ denotes the [[gamma function]].
  
 
<div align="center">
 
<div align="center">
 
<gallery>
 
<gallery>
File:Complex Reciprocal Gamma.jpg|[[Domain coloring]] of [[analytic continuation]] $\dfrac{1}{\Gamma}$.
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File:Reciprocalgammaplotonneg4to10.png|Graph of $\dfrac{1}{\Gamma}$ on $[-4,10]$.
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File:Reciprocalgammaplotonneg7.5to5.1.png|Graph of $\dfrac{1}{\Gamma}$ on $[-7.5,5.1]$.
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File:Complexreciprocalgammaplot.png|[[Domain coloring]] of $\dfrac{1}{\Gamma}$.
 
File:Gamma and reciprocal gamma (abramowitzandstegun).png|Plot of [[Gamma function|$\Gamma$]] and $\dfrac{1}{\Gamma}$ from Abramowitz&Stegun.
 
File:Gamma and reciprocal gamma (abramowitzandstegun).png|Plot of [[Gamma function|$\Gamma$]] and $\dfrac{1}{\Gamma}$ from Abramowitz&Stegun.
 
</gallery>
 
</gallery>
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=Properties=
 
=Properties=
{{:Gamma function Weierstrass product}}
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[[Reciprocal gamma is entire]]<br />
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[[Reciprocal gamma written as an infinite product]]<br />
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[[Contour integral representation of reciprocal gamma]]<br />
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=See Also=
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[[Fransén–Robinson constant]]<br />
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[[Gamma function]] <br />
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[[Category:SpecialFunction]]

Latest revision as of 10:50, 11 January 2017

The reciprocal gamma function $\dfrac{1}{\Gamma}$ is defined by $$\left( \dfrac{1}{\Gamma} \right)(z) =\dfrac{1}{\Gamma(z)},$$ where $\Gamma$ denotes the gamma function.

Properties

Reciprocal gamma is entire
Reciprocal gamma written as an infinite product
Contour integral representation of reciprocal gamma

See Also

Fransén–Robinson constant
Gamma function