DLMF:19.23.E9

MaRDI QIDQ7176

• Label: DLMF:19.23.E9

Digital Library of Mathematical Functions ID 19.23.E9

${\displaystyle{\displaystyle R_{-a}\left(\mathbf{b};\mathbf{z}\right)=\frac{4\Gamma\left(b_{1}+b_{2}+b_{3}\right)}{\Gamma\left(b_{1}\right)\Gamma\left(b_{2}\right)\Gamma\left(b_{3}\right)}\int_{0}^{\pi/2}\!\!\!\!\int_{0}^{\pi/2}\left(\sum_{j=1}^{3}z_{j}l_{j}^{2}\right)^{-a}\*\prod_{j=1}^{3}l_{j}^{2b_{j}-1}\sin\theta\mathrm{d}\theta\mathrm{d}\phi,}}$

Constraint(s)

${\displaystyle{\displaystyle\Re z_{j}>0}}$
${\displaystyle{\displaystyle b_{j}>0}}$
${\displaystyle{\displaystyle\Re z_{j}>0}}$

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
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle l}}$: nonnegative integer
• ${\displaystyle{\displaystyle\phi}}$: real or complex argument
 

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