# Polygamma

The polygamma function of order $m$, $\psi^{(m)}(z)$, is defined by the formula $$\psi^{(m)}(z) = \dfrac{\mathrm{d}^{m+1}}{\mathrm{d}z^{m+1}} \log \Gamma(z),$$ where $\log \Gamma$ denotes the loggamma function. The digamma function $\psi$ is the function $\psi^{(0)}(z)$ and the trigamma function is $\psi^{(1)}(z)$.