DLMF:27.14.E10 (Q8109)

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DLMF:27.14.E10
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    Statements

    Defining formula
    A k ⁢ ( n ) = ∑ h = 1 ( h , k ) = 1 k exp ⁡ ( π ⁢ i ⁢ s ⁢ ( h , k ) - 2 ⁢ π ⁢ i ⁢ n ⁢ h k ) , subscript 𝐴 𝑘 𝑛 superscript subscript ℎ 1 ℎ 𝑘 1 𝑘 imaginary-unit 𝑠 ℎ 𝑘 2 imaginary-unit 𝑛 ℎ 𝑘 {\displaystyle{\displaystyle A_{k}(n)=\sum_{\begin{subarray}{c}h=1\\ \left(h,k\right)=1\end{subarray}}^{k}\exp\left(\pi\mathrm{i}s(h,k)-2\pi\mathrm% {i}n\frac{h}{k}\right),}}
    0 references
    DLMF id
    DLMF:27.14.E10
    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
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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    Q12093
    Defining formula
    ( m , n ) 𝑚 𝑛 {\displaystyle{\displaystyle\left(\NVar{m},\NVar{n}\right)}}
    xml-id
    C27.S1.p2.t1.r3.m6adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q12238
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C27.S1.XMD2.m1edec
    0 references
     
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