DLMF:25.2.E6 (Q7601)

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DLMF:25.2.E6
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    Statements

    Defining formula
    ζ ′ ⁡ ( s ) = - ∑ n = 2 ∞ ( ln ⁡ n ) ⁢ n - s , diffop Riemann-zeta 1 𝑠 superscript subscript 𝑛 2 𝑛 superscript 𝑛 𝑠 {\displaystyle{\displaystyle\zeta'\left(s\right)=-\sum_{n=2}^{\infty}(\ln n)n^% {-s},}}
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    DLMF id
    DLMF:25.2.E6
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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.m2addec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
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    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1acdec
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    Q12148
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1edec
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