Mneimneh-type Binomial Sums of Multiple Harmonic-type Sums

2024/03/10 by Ende Pan, Pan, Ende, Ce Xu +1 · 1 citation
Mathematics · #Advanced Mathematical Identities #Advanced Topics in Algebra #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2403.17952

openalex publication_date 2024/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish some expressions of Mneimneh-type binomial sums involving multiple harmonic-type sums in terms of finite sums of Stirling numbers, Bell numbers and some related variables. In particular, we present some new formulas of Mneimneh-type binomial sums involving generalized (alternating) harmonic numbers. Further, we establish a new identity relating the multiple zeta star values ζ^⋆(m+2,\1\_r-1) and specific multiple polylogarithms by applying the Toeplitz principle. Furthermore, we present some interesting consequences and illustrative examples.

Cited by

• A q-analogue of Boyadzhiev-Mneimneh-type binomial sums of finite multi-polylogarithms

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