The digamma function, usually represented by the Greek letter psi or digamma, is the logarithmic derivative of the [tag:gamma-function]. It is the first of the polygamma functions.
$\psi(z)$ is defined as $\psi(z) =\frac{\mathrm{d}}{\mathrm{d}z}\log\Gamma(z)= \frac{\Gamma'(z)}{\Gamma(z)}.$
It has a series expansion converging everywhere except for the negative integers $\psi(z+1) = -\gamma + \sum_{n=1}^\infty \frac{z}{n(n+z)},$ where $\gamma$ is the Euler-Mascheroni constant.
$\psi(z)$ is a special case of the polygamma function $\psi^{(n)}(z)$ where $n=0$.
