Saalsch\"utz's theorem and summation formulae involving generalized harmonic numbers

TL;DR

This paper derives new summation formulas involving generalized harmonic numbers using derivative, integral operators, and Saalschütz's theorem, expanding mathematical tools for harmonic number analysis.

Contribution

It introduces two new families of summation formulas involving generalized harmonic numbers based on classical operators and Saalschütz's theorem.

Findings

Established new summation formulas involving generalized harmonic numbers.

Connected derivative and integral operators with Saalschütz's theorem.

Enhanced methods for analyzing harmonic number sums.

Abstract

In terms of the derivative operator, integral operator and Saalsch\"{u}tz's theorem, two families of summation formulae involving generalized harmonic numbers are established.