Herglotz–Zagier function

In mathematics, the Herglotz–Zagier function,^[1] named after Gustav Herglotz and Don Zagier,^[2] is the function

${\displaystyle F(x)=\sum _{n=1}^{\infty }\left\{{\frac {\Gamma ^{\prime }(nx)}{\Gamma (nx)}}-\log(nx)\right\}{\frac {1}{n}}.}$

It was introduced by Zagier who used it to obtain a Kronecker limit formula for real quadratic fields.^[3]