Reciprocal gamma

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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  Graph of $\dfrac{1}{\Gamma}$ on $[-4,10]$.

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  Graph of $\dfrac{1}{\Gamma}$ on $[-7.5,5.1]$.

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  Domain coloring of $\dfrac{1}{\Gamma}$.

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  Plot of $\Gamma$ and $\dfrac{1}{\Gamma}$ from Abramowitz&Stegun.

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