Gauss's Integral Form of Digamma Function

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


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

where $\psi$ is the digamma function.