DLMF:16.14.E6 (Q5262)

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DLMF:16.14.E6
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    Statements

    Defining formula
    G 3 ⁢ ( α , α ′ ; x , y ) = ∑ m , n = 0 ∞ Γ ⁡ ( α + 2 ⁢ n - m ) ⁢ Γ ⁡ ( α ′ + 2 ⁢ m - n ) Γ ⁡ ( α ) ⁢ Γ ⁡ ( α ′ ) ⁢ x m ⁢ y n m ! ⁢ n ! , subscript 𝐺 3 𝛼 superscript 𝛼 ′ 𝑥 𝑦 superscript subscript 𝑚 𝑛 0 Euler-Gamma 𝛼 2 𝑛 𝑚 Euler-Gamma superscript 𝛼 ′ 2 𝑚 𝑛 Euler-Gamma 𝛼 Euler-Gamma superscript 𝛼 ′ superscript 𝑥 𝑚 superscript 𝑦 𝑛 𝑚 𝑛 {\displaystyle{\displaystyle G_{3}(\alpha,\alpha^{\prime};x,y)=\sum_{m,n=0}^{% \infty}\frac{\Gamma\left(\alpha+2n-m\right)\Gamma\left(\alpha^{\prime}+2m-n% \right)}{\Gamma\left(\alpha\right)\Gamma\left(\alpha^{\prime}\right)}\frac{x^{% m}y^{n}}{m!n!},}}
    0 references
    DLMF id
    DLMF:16.14.E6
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    constraint
    | x | + | y | < 1 4 𝑥 𝑦 1 4 {\displaystyle{\displaystyle|x|+|y|<\frac{1}{4}}}
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
     
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