A generalization of the duality for multiple harmonic sums

TL;DR

This paper extends the duality property of finite multiple harmonic sums to certain generalized forms, providing new formulas for their differences and broadening understanding of their algebraic structure.

Contribution

It introduces a duality result for generalized multiple harmonic sums and derives formulas for their differences, expanding the theoretical framework.

Findings

Proved a duality for generalized multiple harmonic sums.

Derived formulas for differences of these sums.

Extended the algebraic understanding of harmonic sums.

Abstract

The duality is a fundamental property of the finite multiple harmonic sums (MHS). In this paper, we prove a duality result for certain generalizations of MHS which appear naturally as the differences of MHS. We also prove a formula for the differences of these generalized MHS.