DLMF:25.16.E14 (Q7770)

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DLMF:25.16.E14
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    Statements

    Defining formula
    ∑ r = 1 ∞ ∑ k = 1 r 1 r ⁢ k ⁢ ( r + k ) = 5 4 ⁢ ζ ⁡ ( 3 ) , superscript subscript 𝑟 1 superscript subscript 𝑘 1 𝑟 1 𝑟 𝑘 𝑟 𝑘 5 4 Riemann-zeta 3 {\displaystyle{\displaystyle\sum_{r=1}^{\infty}\sum_{k=1}^{r}\frac{1}{rk(r+k)}% =\frac{5}{4}\zeta\left(3\right),}}
    0 references
    DLMF id
    DLMF:25.16.E14
    0 references
    Symbols used
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2ahdec
    0 references
    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1bdec
    0 references
     
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