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3.5#Ex17 - MaRDI portal

3.5#Ex17 (Q1246)

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3.5#Ex17
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    Statements

    DLMF defining formula
    γ n = Γ ⁡ ( n + α + 1 ) ⁢ Γ ⁡ ( n + β + 1 ) ⁢ Γ ⁡ ( n + α + β + 1 ) ( 2 ⁢ n + α + β + 1 ) ⁢ ( Γ ⁡ ( 2 ⁢ n + α + β + 1 ) ) 2 ⁢ 2 2 ⁢ n + α + β + 1 ⁢ n ! , subscript 𝛾 𝑛 Euler-Gamma 𝑛 𝛼 1 Euler-Gamma 𝑛 𝛽 1 Euler-Gamma 𝑛 𝛼 𝛽 1 2 𝑛 𝛼 𝛽 1 superscript Euler-Gamma 2 𝑛 𝛼 𝛽 1 2 superscript 2 2 𝑛 𝛼 𝛽 1 𝑛 {\displaystyle{\displaystyle\gamma_{n}=\dfrac{\Gamma\left(n+\alpha+1\right)% \Gamma\left(n+\beta+1\right)\Gamma\left(n+\alpha+\beta+1\right)}{(2n+\alpha+% \beta+1)(\Gamma\left(2n+\alpha+\beta+1\right))^{2}}2^{2n+\alpha+\beta+1}n!,}}
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    constraint
    β > - 1 𝛽 1 {\displaystyle{\displaystyle\beta>-1}}
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    Identifiers

     
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