Polynomials Related to Harmonic Numbers and Evaluation of Harmonic Number Series II

TL;DR

This paper explores harmonic versions of r-geometric and r-exponential polynomials, demonstrating their utility in deriving closed-form expressions for series involving harmonic numbers.

Contribution

It introduces harmonic versions of these polynomials and shows how they can be used to evaluate harmonic number series analytically.

Findings

Derived closed-form expressions for harmonic number series.

Established connections between harmonic polynomials and series evaluation.

Provided new tools for analyzing harmonic number related series.

Abstract

In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. It is shown that harmonic versions of these polynomials and their generalizations are useful to obtain closed forms of some series related to harmonic numbers.