DLMF:18.19.E2 (Q5832)

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DLMF:18.19.E2
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    Statements

    Defining formula
    w ⁢ ( z ; a , b , a ¯ , b ¯ ) = Γ ⁡ ( a + i ⁢ z ) ⁢ Γ ⁡ ( b + i ⁢ z ) ⁢ Γ ⁡ ( a ¯ - i ⁢ z ) ⁢ Γ ⁡ ( b ¯ - i ⁢ z ) , 𝑤 𝑧 𝑎 𝑏 𝑎 𝑏 Euler-Gamma 𝑎 𝑖 𝑧 Euler-Gamma 𝑏 𝑖 𝑧 Euler-Gamma 𝑎 𝑖 𝑧 Euler-Gamma 𝑏 𝑖 𝑧 {\displaystyle{\displaystyle w(z;a,b,\overline{a},\overline{b})=\Gamma\left(a+% iz\right)\Gamma\left(b+iz\right)\Gamma\left(\overline{a}-iz\right)\Gamma\left(% \overline{b}-iz\right),}}
    0 references
    DLMF id
    DLMF:18.19.E2
    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.m2adec
    0 references
    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2aadec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    Q11729
    Defining formula
    w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    xml-id
    C18.S1.XMD10.m1dec
    0 references
     
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