Series representations for the Stieltjes constants
M. Coffey. (2009)cite arxiv:0905.1111Comment: 37 pages, no figures New material added at end, including Corollary 6.
Аннотация
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.
Описание
Series representations for the Stieltjes constants
%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
}