DLMF:23.22.E3 (Q7390)

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DLMF:23.22.E3
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    Statements

    Defining formula
    2 ⁢ ω 1 = 2 ⁢ e - π ⁢ i / 3 ⁢ ω 3 = ( Γ ⁡ ( 1 3 ) ) 3 2 ⁢ π ⁢ d 1 / 6 . 2 subscript 𝜔 1 2 superscript 𝑒 𝜋 𝑖 3 subscript 𝜔 3 superscript Euler-Gamma 1 3 3 2 𝜋 superscript 𝑑 1 6 {\displaystyle{\displaystyle 2\omega_{1}=2e^{-\pi i/3}\omega_{3}=\frac{\left(% \Gamma\left(\frac{1}{3}\right)\right)^{3}}{2\pi d^{1/6}}.}}
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    DLMF id
    DLMF:23.22.E3
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
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    Q12049
    Defining formula
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    xml-id
    C23.S1.XMD8.m1bdec
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