DLMF:27.4.E13 (Q8024)

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DLMF:27.4.E13
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    Statements

    test
    ∑ n = 2 ∞ ( ln ⁡ n ) ⁢ n - s = - ζ ′ ⁡ ( s ) , superscript subscript 𝑛 2 𝑛 superscript 𝑛 𝑠 diffop Riemann-zeta 1 𝑠 {\displaystyle{\displaystyle\sum_{n=2}^{\infty}(\ln n)n^{-s}=-\zeta'\left(s% \right),}}
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    DLMF id
    DLMF:27.4.E13
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    constraint
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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    Symbols used
    Riemann zeta function
    test
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2aidec
    0 references
     
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