DLMF:16.15.E1 (Q5263)

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Language	Label	Description	Also known as
English	DLMF:16.15.E1	No description defined

Statements

Defining formula

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

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DLMF:16.15.E1

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

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{\displaystyle{\displaystyle\Re(\gamma-\alpha)>0}}

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first Appell function

Defining formula

{\displaystyle{\displaystyle{F_{1}}\left(\NVar{\alpha};\NVar{\beta},\NVar{% \beta^{\prime}};\NVar{\gamma};missing,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}

C16.S13.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3adec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1adec

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