DLMF:16.15.E1 (Q5263)

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DLMF:16.15.E1
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    Statements

    Defining formula
    F 1 ⁡ ( α ; β , β ′ ; γ ; x , y ) = Γ ⁡ ( γ ) Γ ⁡ ( α ) ⁢ Γ ⁡ ( γ - α ) ⁢ ∫ 0 1 u α - 1 ⁢ ( 1 - u ) γ - α - 1 ( 1 - u ⁢ x ) β ⁢ ( 1 - u ⁢ y ) β ′ ⁢ d u , Appell-F-1 𝛼 𝛽 superscript 𝛽 ′ 𝛾 𝑥 𝑦 Euler-Gamma 𝛾 Euler-Gamma 𝛼 Euler-Gamma 𝛾 𝛼 superscript subscript 0 1 superscript 𝑢 𝛼 1 superscript 1 𝑢 𝛾 𝛼 1 superscript 1 𝑢 𝑥 𝛽 superscript 1 𝑢 𝑦 superscript 𝛽 ′ 𝑢 {\displaystyle{\displaystyle{F_{1}}\left(\alpha;\beta,\beta^{\prime};\gamma;x,% y\right)=\frac{\Gamma\left(\gamma\right)}{\Gamma\left(\alpha\right)\Gamma\left% (\gamma-\alpha\right)}\int_{0}^{1}\frac{u^{\alpha-1}(1-u)^{\gamma-\alpha-1}}{(% 1-ux)^{\beta}(1-uy)^{\beta^{\prime}}}\mathrm{d}u,}}
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    DLMF id
    DLMF:16.15.E1
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