Harmonic-Number Summation Identities, Symmetric Functions, and Multiple Zeta Values

TL;DR

This paper develops methods to evaluate infinite series involving harmonic numbers using symmetric functions and multiple zeta values, proving and generalizing several recent conjectures and discovering new identities.

Contribution

It introduces a novel approach connecting harmonic series with symmetric functions and multiple zeta values, extending known identities and proposing new families of such identities.

Findings

Proved and generalized identities conjectured by J. Choi.

Developed a method to compute series involving harmonic numbers.

Discovered new families of harmonic number identities.

Abstract

We show how infinite series of a certain type involving generalized harmonic numbers can be computed using a knowledge of symmetric functions and multiple zeta values. In particular, we prove and generalize some identities recently conjectured by J. Choi, and give several more families of identities of a similar nature.