Series of zeta values, the Stieltjes constants, and a sum Sγ(n)
Abstract
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 Sγ(n) formed as an alternating binomial series from the Stieltjes constants. The slowly varying sum Sγ(n)+n is an important subsum in application of the Li criterion for the Riemann hypothesis.
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