Series of zeta values, the Stieltjes constants, and a sum S_γ(n)
Abstract
Description
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_γ(n) formed as an alternating binomial series from the Stieltjes constants. The slowly varying sum S_γ(n)+n is an important subsum in application of the Li criterion for the Riemann hypothesis.
33 pages, no figures. Prop. 1(b) typos fixed and proof elaborated. New section with Corollary 1 added. Minor updates
33 pages, no figures. Prop. 1(b) typos fixed and proof elaborated. New section with Corollary 1 added. Minor updates