Formula:2689

Digital Library of Mathematical Functions ID 5.9.E15

${\displaystyle{\displaystyle\psi\left(z\right)=\ln z-\frac{1}{2z}-2\int_{0}^{\infty}\frac{t\mathrm{d}t}{(t^{2}+z^{2})(e^{2\pi t}-1)}.}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: 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
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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