Comment on a paper "Watson - like Formulae for terminating $_{3}F_2$ series" by Chu and Zhou

TL;DR

This paper comments on a recent work by Chu and Zhou that presented 40 closed-form formulas for terminating Watson-like hypergeometric $_{3}F_2$ series, noting that most of these results were previously discovered in 1992.

Contribution

It highlights that 33 of the 40 formulas in Chu and Zhou's paper were already known, providing a historical correction and clarification.

Findings

33 of 40 formulas were previously discovered in 1992

Chu and Zhou's work rederives known formulas

The note clarifies the novelty of recent results

Abstract

In a recent paper, Chu and Zhou [Advances in Combinatorics, I.S. Kotsireas and E.V. Zima(eds.), 139-159 (2013)] established in all 40 closed formulae for terminating Watson-like hypergeometric $_{3}F_2$- series by investigating through Gould and Hsu's fundamental pair of inverse series relations, the dual relations of Dougall's formula for the very well - poised $_{5}F_4$ - series. The aim of this short note is just to point out that out of 40 results, 33 results have already been discovered in 1992 by Lavoie, et al.