Herglotz–Zagier function: Difference between revisions
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In mathematics, the '''Herglotz–Zagier function''' is the function |
In mathematics, the '''Herglotz–Zagier function''', named after [[Gustav Herglotz]] and [[Don Zagier]], is the function |
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:<math>F(x)= \sum^{\infty}_{n=1} \left\{\frac{\Gamma^{\prime}(nx)}{\Gamma (nx)} -\log (nx)\right\} \frac{1}{n}.</math> |
:<math>F(x)= \sum^{\infty}_{n=1} \left\{\frac{\Gamma^{\prime}(nx)}{\Gamma (nx)} -\log (nx)\right\} \frac{1}{n}.</math> |
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Revision as of 16:52, 24 March 2010
In mathematics, the Herglotz–Zagier function, named after Gustav Herglotz and Don Zagier, is the function
introduced by Zagier (1975) who used to to obtain a Kronecker limit formula for real quadratic fields.
References
- Herglotz, G. (1923), Ber. Verh. Sächs. Gesellschaft. Wiss. Leipzig Math.-Phys. Kl., 75: 3–14
{{citation}}: 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, MR2059072
- Zagier, Don (1975), "A Kronecker limit formula for real quadratic fields", Mathematische Annalen, 213: 153–184, doi:10.1007/BF01343950, ISSN 0025-5831, MR0366877