Digamma function

Summary

The digamma function $\psi$ is the logarithmic derivative of the gamma function, $\psi(z) = \Gamma'(z)/\Gamma(z)$. It turns the product rule $\Gamma(z+1) = z\,\Gamma(z)$ into the sum rule $\psi(z+1) = \psi(z) + 1/z$. At positive integers it gives the harmonic numbers shifted by the Euler–Mascheroni constant. It is the first member of the family of polygamma functions.