Pfaff's Method Revisited

TL;DR

This paper revisits Pfaff's method, demonstrating its effectiveness in proving various terminating q-hypergeometric series identities, thus showcasing its broad applicability in hypergeometric series theory.

Contribution

It provides a comprehensive demonstration of Pfaff's method applied to q-hypergeometric identities, expanding its known applications.

Findings

Proved multiple terminating q-hypergeometric series identities

Showcased the wide applicability of Pfaff's method

Connected historical and modern hypergeometric results

Abstract

In 1797, Pfaff gave a simple proof of a ${}_3F_2$ hypergeometric series summation formula which was much later reproved by Andrews in 1996. In the same paper, Andrews also proved other well-known hypergeometric identities using Pfaff's method. In this paper, we prove a number of terminating $q$-hypergeometric series-product identities using Pfaff's method thereby providing a detailed account of its wide applicability.