Formula:DLMF:25.16:E15

<< Formula:DLMF:25.16:E14

formula in Mathematical Applications

Zeta and Related Functions

${\displaystyle{\displaystyle{\displaystyle\sum_{r=1}^{\infty}\sum_{k=1}^{r}\frac{1}{r^{2}(r+k)}=\frac{3}{4}\RiemannZeta@{3}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Riemann zeta function : http://dlmf.nist.gov/25.2#E1

Bibliography

Equation (15), Section 25.16 of DLMF.

URL links

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<< Formula:DLMF:25.16:E14

formula in Zeta and Related Functions

Zeta and Related Functions