DLMF:16.13.E3 (Q5251)

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DLMF:16.13.E3
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    Statements

    Defining formula
    F 3 ⁡ ( α , α ′ ; β , β ′ ; γ ; x , y ) = ∑ m , n = 0 ∞ ( α ) m ⁢ ( α ′ ) n ⁢ ( β ) m ⁢ ( β ′ ) n ( γ ) m + n ⁢ m ! ⁢ n ! ⁢ x m ⁢ y n , Appell-F-3 𝛼 superscript 𝛼 ′ 𝛽 superscript 𝛽 ′ 𝛾 𝑥 𝑦 superscript subscript 𝑚 𝑛 0 Pochhammer 𝛼 𝑚 Pochhammer superscript 𝛼 ′ 𝑛 Pochhammer 𝛽 𝑚 Pochhammer superscript 𝛽 ′ 𝑛 Pochhammer 𝛾 𝑚 𝑛 𝑚 𝑛 superscript 𝑥 𝑚 superscript 𝑦 𝑛 {\displaystyle{\displaystyle{F_{3}}\left(\alpha,\alpha^{\prime};\beta,\beta^{% \prime};\gamma;x,y\right)=\sum_{m,n=0}^{\infty}\frac{{\left(\alpha\right)_{m}}% {\left(\alpha^{\prime}\right)_{n}}{\left(\beta\right)_{m}}{\left(\beta^{\prime% }\right)_{n}}}{{\left(\gamma\right)_{m+n}}m!n!}x^{m}y^{n},}}
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    DLMF id
    DLMF:16.13.E3
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    constraint
    max ⁡ ( | x | , | y | ) < 1 𝑥 𝑦 1 {\displaystyle{\displaystyle\max\left(|x|,|y|\right)<1}}
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