Some notes on an identity of Frisch

TL;DR

This paper explores a combinatorial identity by Frisch, applying it to prove and extend identities related to harmonic numbers, including those involving odd harmonic numbers, offering new insights and generalizations.

Contribution

It introduces a novel application of Frisch's combinatorial identity to harmonic number identities and derives new identities involving odd harmonic numbers.

Findings

Generalized harmonic number identities using Frisch's identity

Derived identities involving odd harmonic numbers

Extended known harmonic number relations

Abstract

In this note, we show how a combinatorial identity of Frisch can be applied to prove and generalize some well-known identities involving harmonic numbers. We also present some combinatorial identities involving odd harmonic numbers which can be inferred straightforwardly from our results.