Formula:8355

Digital Library of Mathematical Functions ID 25.8.E5

${\displaystyle{\displaystyle\sum_{k=2}^{\infty}\zeta\left(k\right)z^{k}=-\gamma z-z\psi\left(1-z\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|z|<1}}$

Symbols List

• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: Riemann zeta function
• ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$: psi (or digamma) function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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