Gauss's Integral Form of Digamma Function

Theorem
Let $z$ be a complex number with a positive real part, then:


 * $\displaystyle \psi\left({z}\right) = \int_0^\infty \left( { \frac{ e^{-t} } t - \frac{ e^{-zt} } { 1 - e^{-t} } } \right) \, \mathrm d t$

where $\psi$ is the digamma function.