Whipple-type $_3F_2$-series and summation formulae involving generalized harmonic numbers

TL;DR

This paper derives new summation formulas involving generalized harmonic numbers using derivative operators and Whipple-type $_3F_2$-series identities, expanding the mathematical tools available for such series.

Contribution

It introduces two new families of summation formulas involving generalized harmonic numbers based on Whipple-type $_3F_2$-series identities.

Findings

Established two families of summation formulas involving generalized harmonic numbers.

Utilized derivative operators and $_3F_2$-series identities to derive these formulas.

Enhanced understanding of relationships between harmonic numbers and hypergeometric series.

Abstract

By means of the derivative operator and Whipple-type $_3F_2$-series identities, two families of summation formulae involving generalized harmonic numbers are established.