Definition:Polygamma Function

Definition
The $n$th polygamma function, $\psi_n$, is defined, for $z \in \C \setminus \Z_{\le 0}$, by the $n$th derivative of the digamma function:


 * $\map {\psi_n} z = \dfrac {\d^n} {\d z^n} \map \psi z$

where $\psi$ is the digamma function.