Formula:8353

Digital Library of Mathematical Functions ID 25.8.E3

${\displaystyle{\displaystyle\sum_{k=0}^{\infty}\frac{{\left(s\right)_{k}}\zeta\left(s+k\right)}{k!2^{s+k}}=(1-2^{-s})\zeta\left(s\right),}}$

Constraint(s)

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

Symbols List

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

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