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.

$\psi$ is defined as $$ \psi(z) = \frac{\Gamma'(z)}{\Gamma(z)} $$ 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.