DLMF:27.10.E4 (Q8061)

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DLMF:27.10.E4
No description defined

    Statements

    Defining formula
    c k ⁡ ( n ) = ∑ m = 1 k χ 1 ⁡ ( m ) ⁢ e 2 ⁢ π ⁢ i ⁢ m ⁢ n / k , Ramanujan-sum 𝑘 𝑛 superscript subscript 𝑚 1 𝑘 Dirichlet-character 1 𝑚 𝑘 superscript 𝑒 2 imaginary-unit 𝑚 𝑛 𝑘 {\displaystyle{\displaystyle c_{k}\left(n\right)=\sum_{m=1}^{k}\chi_{1}\left(m% \right)e^{2\pi\mathrm{i}mn/k},}}
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    DLMF id
    DLMF:27.10.E4
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    Symbols used
    Q12252
    Defining formula
    χ ⁡ ( n ) Dirichlet-character 𝑛 𝑘 {\displaystyle{\displaystyle\chi\left(\NVar{n}\right)}}
    xml-id
    C27.S8.m1adec
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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.m2abdec
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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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    Q12238
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C27.S1.XMD2.m1cdec
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    Q12239
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C27.S1.XMD3.m1bdec
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    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1cdec
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    Q12259
    Defining formula
    χ Dirichlet-character {\displaystyle{\displaystyle\chi}}
    xml-id
    C27.S10.XMD5.m1dec
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