Summation formulas involving harmonic numbers with even or odd indexes

TL;DR

This paper derives new summation formulas involving harmonic numbers with even or odd indexes using derivative operators and Chu-Vandermonde convolution techniques.

Contribution

It introduces four new families of summation formulas involving harmonic numbers with even or odd indexes, expanding existing mathematical identities.

Findings

Four new summation formulas involving harmonic numbers.

Formulas applicable to even and odd indexed harmonic numbers.

Methodology based on derivative operators and Chu-Vandermonde convolution.

Abstract

By means of the derivative operator and Chu-Vandermonde convolution, four families of summation formulas involving harmonic numbers with even or odd indexes are established.