DLMF:16.13.E2 (Q5250)

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DLMF:16.13.E2
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    F 2 ( α ; β , β ; γ , γ ; x , y ) = m , n = 0 ( α ) m + n ( β ) m ( β ) n ( γ ) m ( γ ) n m ! n ! x m y n , Appell-F-2 𝛼 𝛽 superscript 𝛽 𝛾 superscript 𝛾 𝑥 𝑦 superscript subscript 𝑚 𝑛 0 Pochhammer 𝛼 𝑚 𝑛 Pochhammer 𝛽 𝑚 Pochhammer superscript 𝛽 𝑛 Pochhammer 𝛾 𝑚 Pochhammer superscript 𝛾 𝑛 𝑚 𝑛 superscript 𝑥 𝑚 superscript 𝑦 𝑛 {\displaystyle{\displaystyle{F_{2}}\left(\alpha;\beta,\beta^{\prime};\gamma,% \gamma^{\prime};x,y\right)=\sum_{m,n=0}^{\infty}\frac{{\left(\alpha\right)_{m+% n}}{\left(\beta\right)_{m}}{\left(\beta^{\prime}\right)_{n}}}{{\left(\gamma% \right)_{m}}{\left(\gamma^{\prime}\right)_{n}}m!n!}x^{m}y^{n},}}
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    DLMF:16.13.E2
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    | x | + | y | < 1 𝑥 𝑦 1 {\displaystyle{\displaystyle|x|+|y|<1}}
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    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    C5.S2.SS3.m1aadec
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