\begin{definition}[Definition:Digamma Function]
The '''digamma function''', $\psi$, is defined, for $z \in \C \setminus \Z_{\le 0}$, by the logarithmic derivative of the gamma function: 
:$\map \psi z = \dfrac {\map {\Gamma'} z} {\map \Gamma z}$
where $\Gamma$ is the gamma function, and $\Gamma'$ denotes its derivative.
\end{definition}