DLMF:18.19.E3 (Q5833)

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DLMF:18.19.E3
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    Statements

    test
    w ⁢ ( x ) = w ⁢ ( x ; a , b , a ¯ , b ¯ ) = | Γ ⁡ ( a + i ⁢ x ) ⁢ Γ ⁡ ( b + i ⁢ x ) | 2 , 𝑤 𝑥 𝑤 𝑥 𝑎 𝑏 𝑎 𝑏 superscript Euler-Gamma 𝑎 imaginary-unit 𝑥 Euler-Gamma 𝑏 imaginary-unit 𝑥 2 {\displaystyle{\displaystyle w(x)=w(x;a,b,\overline{a},\overline{b})=|\Gamma% \left(a+\mathrm{i}x\right)\Gamma\left(b+\mathrm{i}x\right)|^{2},}}
    0 references
    DLMF id
    DLMF:18.19.E3
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    complex conjugate
    test
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2abdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q11729
    test
    w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    xml-id
    C18.S1.XMD10.m1adec
    0 references
    Q11727
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1cdec
    0 references
     
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