DLMF:16.15.E3 (Q5265)

No description defined

Language	Label	Description	Also known as
English	DLMF:16.15.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{F_{3}}\left(\alpha,\alpha^{\prime};\beta,\beta^{% \prime};\gamma;x,y\right)=\frac{\Gamma\left(\gamma\right)}{\Gamma\left(\beta% \right)\Gamma\left(\beta^{\prime}\right)\Gamma\left(\gamma-\beta-\beta^{\prime% }\right)}\iint_{\Delta}\frac{u^{\beta-1}v^{\beta^{\prime}-1}(1-u-v)^{\gamma-% \beta-\beta^{\prime}-1}}{(1-ux)^{\alpha}(1-vy)^{\alpha^{\prime}}}\mathrm{d}u% \mathrm{d}v,}}

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DLMF id

DLMF:16.15.E3

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constraint

{\displaystyle{\displaystyle\Re(\gamma-\beta-\beta^{\prime})>0}}

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{\displaystyle{\displaystyle\Re\beta>0}}

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

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Symbols used

third Appell function

Defining formula

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "XMLReader::XML(): Argument #1 ($source) cannot be empty"): {\displaystyle \AppellF{3}@{\NVar{\alpha}}{\NVar{\alpha^{\prime}}}{\NVar{\beta}}{\NVar{\beta^% {\prime}}}{\NVar{\gamma}}{\NVar{x}}{\NVar{y}}}

xml-id

C16.S13.E3.m2adec

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gamma function

Defining formula