Formula:2691

Digital Library of Mathematical Functions ID 5.9.E16

${\displaystyle{\displaystyle\psi\left(z\right)+\gamma=\int_{0}^{\infty}\frac{e^{-t}-e^{-zt}}{1-e^{-t}}\mathrm{d}t=\int_{0}^{1}\frac{1-t^{z-1}}{1-t}\mathrm{d}t.}}$

Symbols List

• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$: psi (or digamma) function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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