Formula:2643

Digital Library of Mathematical Functions ID 5.7.E5

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

Constraint(s)

${\displaystyle{\displaystyle z\neq 0,\pm 1}}$

Symbols List

• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: Riemann zeta function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cot\NVar{z}}}$: cotangent function
• ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$: psi (or digamma) function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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