Formula:DLMF:25.8:E2

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formula in Sums

Formula:DLMF:25.8:E3 >>

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

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle s\neq 1,0,-1,-2,\dots}}}$

Proof

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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 (2), Section 25.8 of DLMF.

URL links

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