Year: 2024
Type: preprint
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 $ζ^\star(m+2,\{1\}_{r-1})$ and specific multiple polylogarithms by applying the Toeplitz principle. Furthermore, we present some interesting consequences and illustrative examples.
Source: arXiv (Cornell University)
Authors: Pan, Ende, Xu, Ce
Institutions: Quzhou University, Anhui Normal University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2887741622, G7167558053, G8775904214
OpenAlex ID: W4393334846