DLMF:19.23.E9 (Q6480): Difference between revisions

Revision as of 14:03, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:19.23.E9	No description defined

{\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,}}

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DLMF:19.23.E9

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

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{\displaystyle{\displaystyle b_{j}>0}}

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

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{\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}% };\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}

C19.S16.E9.m2aadec

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@@ Property / Symbols used @@
+multivariate hypergeometric function
@@ Property / Symbols used: multivariate hypergeometric function / rank @@
+Normal rank
@@ Property / Symbols used: multivariate hypergeometric function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}% };\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}$ 
\Carlsonmultivarhyper{\NVar{-a}}@{\NVar{b_{1}},\dots,\NVar{b_{n}}}{\NVar{z_{1}},\dots,\NVar{z_{n}}}
@@ Property / Symbols used: multivariate hypergeometric function / qualifier @@
+xml-id: C19.S16.E9.m2aadec