Formula:DLMF:25.16:E9

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formula in Mathematical Applications

Formula:DLMF:25.16:E10 >>

${\displaystyle{\displaystyle{\displaystyle\EulerSumH@{a}=\frac{a+2}{2}\RiemannZeta@{a+1}-\frac{1}{2}\sum_{r=1}^{a-2}\RiemannZeta@{r+1}\RiemannZeta@{a-r}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle a=2,3,4,\dots}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle H}}}$ : Euler sums : http://dlmf.nist.gov/25.16#SS2.p1
${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Riemann zeta function : http://dlmf.nist.gov/25.2#E1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum

Bibliography

Equation (9), Section 25.16 of DLMF.

URL links

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