DLMF:5.4.E3 (Q2039)

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DLMF:5.4.E3
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    Statements

    test
    | Γ ⁡ ( i ⁢ y ) | = ( π y ⁢ sinh ⁡ ( π ⁢ y ) ) 1 / 2 , Euler-Gamma 𝑖 𝑦 superscript 𝜋 𝑦 𝜋 𝑦 1 2 {\displaystyle{\displaystyle|\Gamma\left(iy\right)|=\left(\frac{\pi}{y\sinh% \left(\pi y\right)}\right)^{1/2},}}
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    DLMF id
    DLMF:5.4.E3
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    hyperbolic sine function
    test
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2adec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    Q11278
    test
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C5.S1.XMD6.m1dec
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