Formula:5931

Digital Library of Mathematical Functions ID 16.11.E2

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle H_{p,q}(z)=\sum_{m=1}^{p}\sum_{k=0}^{\infty}\frac{(-1)^{k}}{k!}\EulerGamma@{a_{m}+k}\left({\textstyle\ifrac{\prod\limits_{\begin{subarray}{c}\ell=1\\ \ell\neq m\end{subarray}}^{p}\EulerGamma@{a_{\ell}-a_{m}-k}}{\prod\limits_{\ell=1}^{q}\EulerGamma@{b_{\ell}-a_{m}-k}}}\right)z^{-a_{m}-k}.}

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle p}}$: 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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