Identities for the shifted harmonic numbers and binomial coefficients

TL;DR

This paper introduces new closed-form formulas for sums involving shifted harmonic numbers and reciprocal binomial coefficients, revealing novel relationships and providing illustrative examples.

Contribution

It presents new closed-form representations of sums involving shifted harmonic numbers and binomial coefficients, expanding the mathematical understanding of these sums.

Findings

New closed-form formulas derived for sums of shifted harmonic numbers.

Identification of interesting consequences and examples illustrating the formulas.

Enhanced understanding of relationships between harmonic numbers and binomial coefficients.

Abstract

We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative examples are considered.