A Note on Harmonic number identities, Stirling series and multiple zeta values

2018/07/02 by Markus Kuba, Kuba, Markus, Alois Panholzer +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1807.00711

openalex publication_date 2018/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a general type of series and relate special cases of it to Stirling series, infinite series discussed by Choi and Hoffman, and also to special values of the Arakawa-Kaneko zeta function, complementing and generalizing earlier results. Moreover, we survey properties of certain truncated multiple zeta and zeta star values, pointing out their relation to finite sums of harmonic numbers. We also discuss the duality result of Hoffman, relating binomial sums and truncated multiple zeta star values.

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