Identities for the q-harmonic numbers and q-binomial coefficients

TL;DR

This paper introduces new q-analog formulas for partial fractions, leading to novel closed-form expressions for sums involving q-harmonic numbers and q-binomial coefficients, expanding the analytical tools for q-series.

Contribution

It develops new q-analog partial fraction formulas and derives explicit, previously unknown closed-form representations for q-harmonic sums and q-binomial coefficient sums.

Findings

New q-analog partial fraction decomposition formula

Explicit formulas for q-harmonic sums in terms of q-polylogarithms

Novel closed-form representations for sums of q-harmonic numbers

Abstract

In this paper, we establish a q-analog of partial fraction decomposition formula. By using formula, we develop new closed form representations of sums of q-harmonic numbers and reciprocal q-binomial coefficients. Moreover, we give explicit formulas for several classes of q- harmonic sums in terms of q-polylogarithms and q-harmonic numbers. The given representations are new.