Pfaff's Method Revisited

2024/05/14 by Aritram Dhar, Dhar, Aritram
Chemistry · #History and advancements in chemistry

paper · pdf · doi:10.48550/arxiv.2405.08705

Abstract

In 1797, Pfaff gave a simple proof of a ₃F₂ 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.

Related

• Basic hypergeometric identities derived from three-term relations
• Multiplicate inverse forms of terminating hypergeometric series
• Nonterminating Basic Hypergeometric Series and the q-Zeilberger Algorithm
• Evaluations of some terminating hypergeometric ₂F₁(2) series
• Reductions of particular hypergeometric functions ₃F₂(a,a+1/3,a+2/3;p/3,q/3;± 1)