DLMF:27.10.E3 (Q8060)

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DLMF:27.10.E3
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    Statements

    Defining formula
    g ⁢ ( m ) = 1 k ⁢ ∑ n = 1 k f ⁢ ( n ) ⁢ e - 2 ⁢ π ⁢ i ⁢ m ⁢ n / k . 𝑔 𝑚 1 𝑘 superscript subscript 𝑛 1 𝑘 𝑓 𝑛 superscript 𝑒 2 imaginary-unit 𝑚 𝑛 𝑘 {\displaystyle{\displaystyle g(m)=\dfrac{1}{k}\sum_{n=1}^{k}f(n)e^{-2\pi% \mathrm{i}mn/k}.}}
    0 references
    DLMF id
    DLMF:27.10.E3
    0 references
    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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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q12238
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C27.S1.XMD2.m1bdec
    0 references
    Q12239
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C27.S1.XMD3.m1adec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1bdec
    0 references
    Q12257
    Defining formula
    f ⁢ ( n ) 𝑓 𝑛 {\displaystyle{\displaystyle f(n)}}
    xml-id
    C27.S10.XMD1.m1bdec
    0 references
    Q12258
    Defining formula
    g ⁢ ( m ) 𝑔 𝑚 {\displaystyle{\displaystyle g(m)}}
    xml-id
    C27.S10.XMD2.m1adec
    0 references
     
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