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

2007/06/03 by Mark W. Coffey, Coffey, Mark W.
Mathematics · #11M06 #11M35 #33B15 #Advanced Mathematical Identities #Advanced Mathematical Theories #Analytic Number Theory Research #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.0706.0345

openalex publication_date 2007/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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