Formula:5909

Digital Library of Mathematical Functions ID 16.5.E1

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \left({\textstyle\ifrac{\prod\limits_{k=1}^{p}\EulerGamma@{a_{k}}}{\prod\limits_{k=1}^{q}\EulerGamma@{b_{k}}}}\right)\genhyperF{p}{q}@@{a_{1},\dots,a_{p}}{b_{1},\dots,b_{q}}{z}=\frac{1}{2\pi\iunit}\int_{L}\left({\textstyle\ifrac{\prod\limits_{k=1}^{p}\EulerGamma@{a_{k}+s}}{\prod\limits_{k=1}^{q}\EulerGamma@{b_{k}+s}}}\right)\EulerGamma@{-s}(-z)^{s}\diff{s},}

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}$: alternatively F q p ( a ; b ; z ) or F q p ( a b ; z ) generalized hypergeometric function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle p}}$: nonnegative integer
• ${\displaystyle{\displaystyle q}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}$: real or complex parameters
• ${\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}$: real or complex parameters
 

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