DLMF:20.11.E1 (Q6842)

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DLMF:20.11.E1
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    Statements

    Defining formula
    G ⁢ ( m , n ) = ∑ k = 0 n - 1 e - π ⁢ i ⁢ k 2 ⁢ m / n ; 𝐺 𝑚 𝑛 superscript subscript 𝑘 0 𝑛 1 superscript 𝑒 𝜋 𝑖 superscript 𝑘 2 𝑚 𝑛 {\displaystyle{\displaystyle G(m,n)=\sum\limits_{k=0}^{n-1}e^{-\pi ik^{2}m/n};}}
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    DLMF id
    DLMF:20.11.E1
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    comment
    Warning: Falling back to standard tex;
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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.m2adec
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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.m2adec
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    Q11951
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C20.S1.XMD1.m1dec
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    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1dec
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