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Research Article | Open Access

Evaluations of some infinite series involving r-Stirling numbers and harmonic numbers

School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
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Abstract

In this paper, we study infinite series involving r-Stirling numbers of the first kind and harmonic numbers. As a result, we establish the integral expressions for three parametric r-Stirling series, and show that these series are ultimately reducible to alternating multiple zeta values (AMZVs). As applications, the explicit AMZV expressions for some parametric series are determined, including some results presented by Wang and Chen, and some results similar to those of Hoffman.

Keywords

infinite series identitiesr-Stirling numbers of the first kindharmonic numbersalternating multiple zeta values
CLC number: 05A19, 40A25, 11B73, 11M32

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AIMS Mathematics
Volume 11 Issue 4,
April 2026
Pages 11977-11992
DOI: 10.3934/math.2026491

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Chen X. Evaluations of some infinite series involving r-Stirling numbers and harmonic numbers. AIMS Mathematics, 2026, 11(4): 11977-11992. https://doi.org/10.3934/math.2026491

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Received: 05 January 2026
Revised: 21 April 2026
Accepted: 22 April 2026
Published: 28 April 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)