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.
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