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DLMF:16.16.E8 - MaRDI portal

DLMF:16.16.E8 (Q5971)

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DLMF:16.16.E8
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    F 1 ( α ; β , β ; γ ; x , y ) = ( 1 - x ) - β ( 1 - y ) - β F 1 ( γ - α ; β , β ; γ ; x x - 1 , y y - 1 ) = ( 1 - x ) - α F 1 ( α ; γ - β - β , β ; γ ; x x - 1 , y - x 1 - x ) , Appell-F-1 𝛼 𝛽 superscript 𝛽 𝛾 𝑥 𝑦 superscript 1 𝑥 𝛽 superscript 1 𝑦 superscript 𝛽 Appell-F-1 𝛾 𝛼 𝛽 superscript 𝛽 𝛾 𝑥 𝑥 1 𝑦 𝑦 1 superscript 1 𝑥 𝛼 Appell-F-1 𝛼 𝛾 𝛽 superscript 𝛽 superscript 𝛽 𝛾 𝑥 𝑥 1 𝑦 𝑥 1 𝑥 {\displaystyle{\displaystyle{F_{1}}\left(\alpha;\beta,\beta^{\prime};\gamma;x,% y\right)=(1-x)^{-\beta}(1-y)^{-\beta^{\prime}}{F_{1}}\left(\gamma-\alpha;\beta% ,\beta^{\prime};\gamma;\frac{x}{x-1},\frac{y}{y-1}\right)=(1-x)^{-\alpha}{F_{1% }}\left(\alpha;\gamma-\beta-\beta^{\prime},\beta^{\prime};\gamma;\frac{x}{x-1}% ,\frac{y-x}{1-x}\right),}}
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    F 1 ( α ; β , β ; γ ; missing , missing ) Appell-F-1 𝛼 𝛽 superscript 𝛽 𝛾 missing missing {\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.m2acdec
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