Formula:2615

Digital Library of Mathematical Functions ID 5.5.E9

${\displaystyle{\displaystyle\psi\left(nz\right)=\frac{1}{n}\sum_{k=0}^{n-1}\psi\left(z+\frac{k}{n}\right)+\ln n.}}$

Symbols List

• ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$: psi (or digamma) function
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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