DLMF:18.19.E4 (Q5834)

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DLMF:18.19.E4
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    Statements

    Defining formula
    h n = 2 ⁢ π ⁢ Γ ⁡ ( n + a + a ¯ ) ⁢ Γ ⁡ ( n + b + b ¯ ) ⁢ | Γ ⁡ ( n + a + b ¯ ) | 2 ( 2 ⁢ n + 2 ⁢ ℜ ⁡ ( a + b ) - 1 ) ⁢ Γ ⁡ ( n + 2 ⁢ ℜ ⁡ ( a + b ) - 1 ) ⁢ n ! , subscript ℎ 𝑛 2 𝜋 Euler-Gamma 𝑛 𝑎 𝑎 Euler-Gamma 𝑛 𝑏 𝑏 superscript Euler-Gamma 𝑛 𝑎 𝑏 2 2 𝑛 2 𝑎 𝑏 1 Euler-Gamma 𝑛 2 𝑎 𝑏 1 𝑛 {\displaystyle{\displaystyle h_{n}=\frac{2\pi\Gamma\left(n+a+\overline{a}% \right)\Gamma\left(n+b+\overline{b}\right)|\Gamma\left(n+a+\overline{b}\right)% |^{2}}{\left(2n+2\Re(a+b)-1\right)\Gamma\left(n+2\Re(a+b)-1\right)n!},}}
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    DLMF id
    DLMF:18.19.E4
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