DLMF:27.4.E6 (Q8017)

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DLMF:27.4.E6
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    Statements

    Defining formula
    ∑ n = 1 ∞ ϕ ⁡ ( n ) ⁢ n - s = ζ ⁡ ( s - 1 ) ζ ⁡ ( s ) , superscript subscript 𝑛 1 Euler-totient-phi 𝑛 superscript 𝑛 𝑠 Riemann-zeta 𝑠 1 Riemann-zeta 𝑠 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}\phi\left(n\right)n^{-s}=\frac{% \zeta\left(s-1\right)}{\zeta\left(s\right)},}}
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    DLMF id
    DLMF:27.4.E6
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    constraint
    ℜ ⁡ s > 2 𝑠 2 {\displaystyle{\displaystyle\Re s>2}}
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    Symbols used
    Euler’s totient
    Defining formula
    ϕ ⁡ ( n ) Euler-totient-phi 𝑛 {\displaystyle{\displaystyle\phi\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E7.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.m2abdec
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    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
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