DLMF:27.4.E12 (Q8023)

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DLMF:27.4.E12
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    Statements

    Defining formula
    ∑ n = 1 ∞ Λ ⁡ ( n ) ⁢ n - s = - ζ ′ ⁡ ( s ) ζ ⁡ ( s ) , superscript subscript 𝑛 1 Mangoldt-Lambda 𝑛 superscript 𝑛 𝑠 diffop Riemann-zeta 1 𝑠 Riemann-zeta 𝑠 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}\Lambda\left(n\right)n^{-s}=-% \frac{\zeta'\left(s\right)}{\zeta\left(s\right)},}}
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    DLMF id
    DLMF:27.4.E12
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    constraint
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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    Symbols used
    Mangoldt’s function
    Defining formula
    Λ ⁡ ( n ) Mangoldt-Lambda 𝑛 {\displaystyle{\displaystyle\Lambda\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E14.m2adec
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    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2ahdec
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    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1ahdec
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    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1kdec
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