Pfaff's Method Revisited

In 1797, Pfaff gave a simple proof of a ${}_3{F}_2$ 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.