Herglotz–Zagier function

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In mathematics, the Herglotz–Zagier function, named after Gustav Herglotz and Don Zagier, is the function

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

introduced by Zagier (1975) who used it to obtain a Kronecker limit formula for real quadratic fields.

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