Abstract
The Stieltjes constants appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function about . We present series representations of these constants of interest to theoretical and computational analytic number theory. A particular result gives an addition formula for the Stieltjes constants. As a byproduct, expressions for derivatives of all orders of the Stieltjes coefficients are given. Many other results are obtained, including instances of an exponentially fast converging series representation for . Some extensions are briefly described, as well as the relevance to expansions of Dirichlet functions.
Citation
Mark W. Coffey. "Series representations for the Stieltjes constants." Rocky Mountain J. Math. 44 (2) 443 - 477, 2014. https://doi.org/10.1216/RMJ-2014-44-2-443
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