DLMF:25.6.E5 (Q7642)

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DLMF:25.6.E5
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    Statements

    Defining formula
    ζ ⁡ ( k + 1 ) = 1 k ! ⁢ ∑ n 1 = 1 ∞ … ⁢ ∑ n k = 1 ∞ 1 n 1 ⁢ ⋯ ⁢ n k ⁢ ( n 1 + … + n k ) , Riemann-zeta 𝑘 1 1 𝑘 superscript subscript subscript 𝑛 1 1 … superscript subscript subscript 𝑛 𝑘 1 1 subscript 𝑛 1 ⋯ subscript 𝑛 𝑘 subscript 𝑛 1 … subscript 𝑛 𝑘 {\displaystyle{\displaystyle\zeta\left(k+1\right)=\frac{1}{k!}\sum_{n_{1}=1}^{% \infty}\dots\sum_{n_{k}=1}^{\infty}\frac{1}{n_{1}\cdots n_{k}(n_{1}+\dots+n_{k% })},}}
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    DLMF id
    DLMF:25.6.E5
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    constraint
    k = 1 , 2 , 3 , … 𝑘 1 2 3 … {\displaystyle{\displaystyle k=1,2,3,\dots}}
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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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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1dec
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