Formula:5896

Digital Library of Mathematical Functions ID 16.4.E5

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \genhyperF{3}{2}@@{-n,b,c}{1-b-n,1-c-n}{1}=\begin{cases}0,&n=2k+1,\\ \dfrac{(2k)!\EulerGamma@{b+k}\EulerGamma@{c+k}\EulerGamma@{b+c+2k}}{k!\EulerGamma@{b+2k}\EulerGamma@{c+2k}\EulerGamma@{b+c+k}},&n=2k,\\ \end{cases}}

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
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}$: real or complex parameters
 

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