Formula:8356

Digital Library of Mathematical Functions ID 25.8.E6

${\displaystyle{\displaystyle\sum_{k=0}^{\infty}\zeta\left(2k\right)z^{2k}=-\tfrac{1}{2}\pi z\cot\left(\pi z\right),}}$

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
• ${\displaystyle{\displaystyle\cot\NVar{z}}}$: cotangent function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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