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

Mark W. Coffey

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arXiv · 0706.0345

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

Mark W. Coffey

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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 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.

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Mark W. Coffey. 2009-02-25. Series of zeta values, the Stieltjes constants, and a sum S_γ(n). https://arxiv.org/abs/0706.0345

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