DLMF:27.10.E7 (Q8064)

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DLMF:27.10.E7
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    Statements

    Defining formula
    s k ⁢ ( n ) = ∑ m = 1 k a k ⁢ ( m ) ⁢ e 2 ⁢ π ⁢ i ⁢ m ⁢ n / k , subscript 𝑠 𝑘 𝑛 superscript subscript 𝑚 1 𝑘 subscript 𝑎 𝑘 𝑚 superscript 𝑒 2 imaginary-unit 𝑚 𝑛 𝑘 {\displaystyle{\displaystyle s_{k}(n)=\sum_{m=1}^{k}a_{k}(m)e^{2\pi\mathrm{i}% mn/k},}}
    0 references
    DLMF id
    DLMF:27.10.E7
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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.m2acdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    Q12238
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C27.S1.XMD2.m1fdec
    0 references
     
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