Formula:DLMF:25.16:E7: Difference between revisions

${\displaystyle{\displaystyle{\displaystyle\EulerSumH@{s}=\frac{1}{2}% \RiemannZeta@{s+1}+\frac{\RiemannZeta@{s}}{s-1}-\sum_{r=1}^{k}\genfrac{(}{)}{0% .0pt}{}{s+2r-2}{2r-1}\RiemannZeta@{1-2r}\RiemannZeta@{s+2r}-\genfrac{(}{)}{0.0% pt}{}{s+2k}{2k+1}\sum_{n=1}^{\infty}\frac{1}{n}\int_{n}^{\infty}\frac{% \PeriodicBernoulliB{2k+1}@{x}}{x^{s+2k+1}}\mathrm{d}x}}}$

Proof

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