Digamma function
= Digamma function
{wiki}
The digamma function is the logarithmic derivative
$$
\psi(z)=\frac{\Gamma'(z)}{\Gamma(z)}.
$$
Logarithmically differentiating the Weierstrass product gives
$$
\psi(z)=-\gamma-\frac1z
+z\sum_{k=1}^{\infty}\frac1{k(z+k)}.
$$