DLMF:18.25.E7 (Q5922)

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DLMF:18.25.E7
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    Statements

    Defining formula
    w ⁢ ( y 2 ) = 1 2 ⁢ y ⁢ | ∏ j Γ ⁡ ( a j + i ⁢ y ) Γ ⁡ ( 2 ⁢ i ⁢ y ) | 2 , 𝑤 superscript 𝑦 2 1 2 𝑦 superscript subscript product 𝑗 Euler-Gamma subscript 𝑎 𝑗 𝑖 𝑦 Euler-Gamma 2 𝑖 𝑦 2 {\displaystyle{\displaystyle w(y^{2})=\frac{1}{2y}\left|\frac{\prod_{j}\Gamma% \left(a_{j}+iy\right)}{\Gamma\left(2iy\right)}\right|^{2},}}
    0 references
    DLMF id
    DLMF:18.25.E7
    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.m2abdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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    Q11743
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1bdec
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    Q11729
    Defining formula
    w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    xml-id
    C18.S1.XMD10.m1bdec
    0 references
     
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