%0 Generic %1 coffey2009series %A Coffey, Mark W. %D 2009 %K representations series stieltjes constant %T Series representations for the Stieltjes constants %U http://arxiv.org/abs/0905.1111 %X The Stieltjes constants \gamma_k(a) appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function \zeta(s,a) about s=1. 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 \gamma_k=\gamma_k(1). Some extensions are briefly described, as well as the relevance to expansions of Dirichlet L functions.

@misc{coffey2009series, abstract = {The Stieltjes constants \gamma_k(a) appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function \zeta(s,a) about s=1. 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 \gamma_k=\gamma_k(1). Some extensions are briefly described, as well as the relevance to expansions of Dirichlet L functions.}, added-at = {2013-12-23T07:07:34.000+0100}, author = {Coffey, Mark W.}, biburl = {https://www.bibsonomy.org/bibtex/288537e18356971174b6a790ddb64c0a4/aeu_research}, description = {Series representations for the Stieltjes constants}, interhash = {717b7363c902a3f24aa1ee67fc486e97}, intrahash = {88537e18356971174b6a790ddb64c0a4}, keywords = {representations series stieltjes constant}, note = {cite arxiv:0905.1111Comment: 37 pages, no figures New material added at end, including Corollary 6}, timestamp = {2013-12-24T01:10:32.000+0100}, title = {Series representations for the Stieltjes constants}, url = {http://arxiv.org/abs/0905.1111}, year = 2009 }