Formula:7177

Digital Library of Mathematical Functions ID 19.23.E10

${\displaystyle{\displaystyle R_{-a}\left(\mathbf{b};\mathbf{z}\right)=\frac{1}{\mathrm{B}\left(a,a^{\prime}\right)}\int_{0}^{1}u^{a-1}(1-u)^{a^{\prime}-1}\*\prod_{j=1}^{n}(1-u+uz_{j})^{-b_{j}}\mathrm{d}u,}}$

Constraint(s)

${\displaystyle{\displaystyle z_{j}\in\mathbb{C}\setminus(-\infty,0]}}$
${\displaystyle{\displaystyle a+a^{\prime}=\sum_{j=1}^{n}b_{j}}}$
${\displaystyle{\displaystyle z_{j}\in\mathbb{C}\setminus(-\infty,0]}}$

Symbols List

• ${\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}};\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}$: multivariate hypergeometric function
• ${\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}$: beta function
• ${\displaystyle{\displaystyle\mathbb{C}}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}$:
• ${\displaystyle{\displaystyle\setminus}}$:
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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