DLMF:27.4.E10 (Q8021)

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DLMF:27.4.E10
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    Statements

    Defining formula
    ∑ n = 1 ∞ d k ⁡ ( n ) ⁢ n - s = ( ζ ⁡ ( s ) ) k , superscript subscript 𝑛 1 divisor-function-D 𝑘 𝑛 superscript 𝑛 𝑠 superscript Riemann-zeta 𝑠 𝑘 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}d_{k}\left(n\right)n^{-s}=(% \zeta\left(s\right))^{k},}}
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    DLMF id
    DLMF:27.4.E10
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    constraint
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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    Symbols used
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2afdec
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    Q12240
    Defining formula
    d k ⁡ ( n ) divisor-function-D 𝑘 𝑛 {\displaystyle{\displaystyle d_{\NVar{k}}\left(\NVar{n}\right)}}
    xml-id
    C27.S2.SS1.p4.m12adec
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    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1afdec
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    Q12238
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C27.S1.XMD2.m1dec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1idec
    0 references
     
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