Series of zeta values, the Stieltjes constants, and a sum S_γ(n)

Details Series of zeta values, the Stieltjes constants, and a sum S_γ(n) Series of zeta values, the Stieltjes constants, and a sum S_γ(n)

2007-06-03

arxiv.org/abs/0706.0345v2

Physics

Mathematical Physics

33 pages, no figures. Prop. 1(b) typos fixed and proof elaborated. New section with Corollary 1 added. Minor updates

Scientific paper

We present a variety of series representations of the Stieltjes and related constants, the Stieltjes constants being the coefficients of the Laurent expansion of the Hurwitz zeta function zeta(s,a) about s=1. Additionally we obtain series and integral representations of a sum S_\gamma(n) formed as an alternating binomial series from the Stieltjes constants. The slowly varying sum S_\gamma(n)+n is an important subsum in application of the Li criterion for the Riemann hypothesis.

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