DLMF:2.5.E12 (Q788)

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DLMF:2.5.E12
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    Statements

    Defining formula
    a n = 2 n - 1 ⁢ Γ ⁡ ( ν + 1 2 ⁢ n ) Γ 2 ⁡ ( 1 - 1 2 ⁢ n ) ⁢ Γ ⁡ ( 1 + ν - 1 2 ⁢ n ) ⁢ Γ ⁡ ( n ) , subscript 𝑎 𝑛 superscript 2 𝑛 1 Euler-Gamma 𝜈 1 2 𝑛 Euler-Gamma 2 1 1 2 𝑛 Euler-Gamma 1 𝜈 1 2 𝑛 Euler-Gamma 𝑛 {\displaystyle{\displaystyle a_{n}=\frac{2^{n-1}\Gamma\left(\nu+\tfrac{1}{2}n% \right)}{{\Gamma^{2}}\left(1-\tfrac{1}{2}n\right)\Gamma\left(1+\nu-\tfrac{1}{2% }n\right)\Gamma\left(n\right)},}}
    0 references
    DLMF id
    DLMF:2.5.E12
    0 references
    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
    Q11000
    Defining formula
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C2.S5.XMD11.m1adec
    0 references
     
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