DLMF:36.4.E11 (Q9889)

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DLMF:36.4.E11
No description defined

    Statements

    Defining formula
    x + i ⁢ y = - z 2 ⁢ exp ⁡ ( 2 3 ⁢ i ⁢ π ⁢ m ) , 𝑥 𝑖 𝑦 superscript 𝑧 2 2 3 𝑖 𝜋 𝑚 {\displaystyle{\displaystyle x+iy=-z^{2}\exp\left(\tfrac{2}{3}i\pi m\right),}}
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    DLMF id
    DLMF:36.4.E11
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    constraint
    m = 0 , 1 , 2 𝑚 0 1 2 {\displaystyle{\displaystyle m=0,1,2}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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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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    Q12745
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C36.S1.XMD10.m1edec
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    Q12746
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C36.S1.XMD11.m1ddec
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    Q12741
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C36.S1.XMD2.m1dec
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    Q12748
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C36.S1.XMD9.m1fdec
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