DLMF:16.14.E5 (Q5261)

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DLMF:16.14.E5
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    Statements

    test
    G 2 ⁢ ( α , α ′ ; β , β ′ ; x , y ) = ∑ m , n = 0 ∞ Γ ⁡ ( α + m ) ⁢ Γ ⁡ ( α ′ + n ) ⁢ Γ ⁡ ( β + n - m ) ⁢ Γ ⁡ ( β ′ + m - n ) Γ ⁡ ( α ) ⁢ Γ ⁡ ( α ′ ) ⁢ Γ ⁡ ( β ) ⁢ Γ ⁡ ( β ′ ) ⁢ x m ⁢ y n m ! ⁢ n ! , subscript 𝐺 2 𝛼 superscript 𝛼 ′ 𝛽 superscript 𝛽 ′ 𝑥 𝑦 superscript subscript 𝑚 𝑛 0 Euler-Gamma 𝛼 𝑚 Euler-Gamma superscript 𝛼 ′ 𝑛 Euler-Gamma 𝛽 𝑛 𝑚 Euler-Gamma superscript 𝛽 ′ 𝑚 𝑛 Euler-Gamma 𝛼 Euler-Gamma superscript 𝛼 ′ Euler-Gamma 𝛽 Euler-Gamma superscript 𝛽 ′ superscript 𝑥 𝑚 superscript 𝑦 𝑛 𝑚 𝑛 {\displaystyle{\displaystyle G_{2}(\alpha,\alpha^{\prime};\beta,\beta^{\prime}% ;x,y)=\sum_{m,n=0}^{\infty}\frac{\Gamma\left(\alpha+m\right)\Gamma\left(\alpha% ^{\prime}+n\right)\Gamma\left(\beta+n-m\right)\Gamma\left(\beta^{\prime}+m-n% \right)}{\Gamma\left(\alpha\right)\Gamma\left(\alpha^{\prime}\right)\Gamma% \left(\beta\right)\Gamma\left(\beta^{\prime}\right)}\frac{x^{m}y^{n}}{m!n!},}}
    0 references
    DLMF id
    DLMF:16.14.E5
    0 references
    constraint
    | y | < 1 𝑦 1 {\displaystyle{\displaystyle|y|<1}}
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
     
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