DLMF:16.15.E4 (Q5266): Difference between revisions

Revision as of 14:41, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:16.15.E4	No description defined

{\displaystyle{\displaystyle{F_{4}}\left(\alpha,\beta;\gamma,\gamma^{\prime};x% (1-y),y(1-x)\right)=\frac{\Gamma\left(\gamma\right)\Gamma\left(\gamma^{\prime}% \right)}{\Gamma\left(\alpha\right)\Gamma\left(\beta\right)\Gamma\left(\gamma-% \alpha\right)\Gamma\left(\gamma^{\prime}-\beta\right)}\int_{0}^{1}\!\!\!\int_{% 0}^{1}\frac{u^{\alpha-1}v^{\beta-1}(1-u)^{\gamma-\alpha-1}(1-v)^{\gamma^{% \prime}-\beta-1}}{(1-ux)^{\gamma+\gamma^{\prime}-\alpha-1}(1-vy)^{\gamma+% \gamma^{\prime}-\beta-1}(1-ux-vy)^{\alpha+\beta-\gamma-\gamma^{\prime}+1}}% \mathrm{d}u\mathrm{d}v,}}

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DLMF:16.15.E4

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{\displaystyle{\displaystyle\Re\gamma>\Re\alpha>0}}

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{\displaystyle{\displaystyle\Re\gamma^{\prime}>\Re\beta>0}}

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{\displaystyle{\displaystyle{F_{4}}\left(\NVar{\alpha},\NVar{\beta};\NVar{% \gamma},\NVar{\gamma^{\prime}}{missing}{missing};missing,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}

C16.S13.E4.m2adec

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@@ Property / Symbols used @@
+fourth Appell function
@@ Property / Symbols used: fourth Appell function / rank @@
+Normal rank
@@ Property / Symbols used: fourth Appell function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle{F_{4}}\left(\NVar{\alpha},\NVar{\beta};\NVar{% \gamma},\NVar{\gamma^{\prime}}{missing}{missing};missing,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}$ 
\AppellF{4}@{\NVar{\alpha}}{\NVar{\beta}}{\NVar{\gamma}}{\NVar{\gamma^{\prime}% }}{\NVar{x}}{\NVar{y}}
@@ Property / Symbols used: fourth Appell function / qualifier @@
+xml-id: C16.S13.E4.m2adec