Formula:DLMF:25.8:E3

<< Formula:DLMF:25.8:E2

formula in Sums

Formula:DLMF:25.8:E4 >>

${\displaystyle{\displaystyle{\displaystyle\sum_{k=0}^{\infty}\frac{\Gamma\left(s+k\right)\RiemannZeta@{s+k}}{k!\Gamma\left(s\right)2^{s+k}}=(1-2^{-s})\RiemannZeta@{s}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle s\neq 1}}}$

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1
${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Riemann zeta function : http://dlmf.nist.gov/25.2#E1

Bibliography

Equation (3), Section 25.8 of DLMF.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:DLMF:25.8:E2

formula in Sums

Formula:DLMF:25.8:E4 >>