DLMF:25.13.E1 (Q7737)

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DLMF:25.13.E1
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    Statements

    Defining formula
    F ⁡ ( x , s ) ≡ ∑ n = 1 ∞ e 2 ⁢ π ⁢ i ⁢ n ⁢ x n s , equal-by definition periodic-zeta 𝑥 𝑠 superscript subscript 𝑛 1 superscript 𝑒 2 𝜋 𝑖 𝑛 𝑥 superscript 𝑛 𝑠 {\displaystyle{\displaystyle F\left(x,s\right)\equiv\sum_{n=1}^{\infty}\frac{e% ^{2\pi inx}}{n^{s}},}}
    0 references
    DLMF id
    DLMF:25.13.E1
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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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    Q10769
    Defining formula
    ≡ equal-by definition {\displaystyle{\displaystyle\equiv}}
    xml-id
    introduction.Sx4.p1.t1.r9.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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    Q12148
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1dec
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