DLMF:16.16.E7 (Q5273): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:16.16.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{F_{4}}\left(\alpha,\beta;\gamma,\gamma^{\prime};x% (1-y),y(1-x)\right)=\sum_{k=0}^{\infty}\frac{{\left(\alpha\right)_{k}}{\left(% \beta\right)_{k}}{\left(\alpha+\beta-\gamma-\gamma^{\prime}+1\right)_{k}}}{{% \left(\gamma\right)_{k}}{\left(\gamma^{\prime}\right)_{k}}k!}x^{k}y^{k}{{}_{2}% F_{1}}\left({\alpha+k,\beta+k\atop\gamma+k};x\right){{}_{2}F_{1}}\left({\alpha% +k,\beta+k\atop\gamma^{\prime}+k};y\right);}}

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DLMF:16.16.E7

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fourth Appell function

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}}}

C16.S13.E4.m2aadec

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Defining formula

{\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}

C16.S2.m5addec

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Defining formula

{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

C5.S2.SS3.m1adec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5adec

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