Herglotz–Zagier function

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

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

References

Herglotz, G. (1923), Berichte über die Verhandlungen der Königlich-Sächsischen Gesellschaft der Wissenschaften zu Leipzig, Mathematisch-Physische Klasse, 75: 3–14 Missing or empty |title= (help)
Masri, Riad (2004), "The Herglotz–Zagier function, double zeta functions, and values of L-series", Journal of Number Theory, 106 (2): 219–237, ISSN 0022-314X, MR 2059072, doi:10.1016/j.jnt.2004.01.004
Zagier, Don (1975), "A Kronecker limit formula for real quadratic fields", Mathematische Annalen, 213: 153–184, ISSN 0025-5831, MR 0366877, doi:10.1007/BF01343950

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