Formula:DLMF:25.8:E9

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formula in Sums

Formula:DLMF:25.8:E10 >>

${\displaystyle{\displaystyle{\displaystyle\sum_{k=1}^{\infty}\frac{\RiemannZeta@{2k}}{(2k+1)2^{2k}}=\frac{1}{2}-\frac{1}{2}\ln 2}}}$

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
${\displaystyle{\displaystyle{\displaystyle\mathrm{ln}}}}$ : principal branch of logarithm function : http://dlmf.nist.gov/4.2#E2

Bibliography

Equation (9), Section 25.8 of DLMF.

URL links

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