Gauss's Integral Form of Digamma Function

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


 * $\ds \map \psi z = \int_0^\infty \paren {\frac {e^{-t} } t - \frac {e^{-z t} } {1 - e^{-t} } } \rd t$

where $\psi$ is the digamma function.