Formula:8352

Digital Library of Mathematical Functions ID 25.8.E2

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

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: Riemann zeta function
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle s}}$: complex variable
 

Resources that cite this formula

No records found.