Difference between revisions of "Reciprocal gamma"
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| − | The reciprocal gamma function is | + | 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]]. | ||
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=Properties= | =Properties= | ||
| + | [[Reciprocal gamma is entire]]<br /> | ||
[[Reciprocal gamma written as an infinite product]]<br /> | [[Reciprocal gamma written as an infinite product]]<br /> | ||
[[Contour integral representation of reciprocal gamma]]<br /> | [[Contour integral representation of reciprocal gamma]]<br /> | ||
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.
Graph of $\dfrac{1}{\Gamma}$ on $[-4,10]$.
Graph of $\dfrac{1}{\Gamma}$ on $[-7.5,5.1]$.
Domain coloring of $\dfrac{1}{\Gamma}$.
Plot of $\Gamma$ and $\dfrac{1}{\Gamma}$ from Abramowitz&Stegun.
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Properties
Reciprocal gamma is entire
Reciprocal gamma written as an infinite product
Contour integral representation of reciprocal gamma
