Formula:8358

Digital Library of Mathematical Functions ID 25.8.E8

${\displaystyle{\displaystyle\sum_{k=1}^{\infty}\frac{\zeta\left(2k\right)}{k}z^{2k}=\ln\left(\frac{\pi z}{\sin\left(\pi z\right)}\right),}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: Riemann zeta function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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