A new proof for a nonterminating "strange" hypergeometric evaluation of Gasper and Rahman

TL;DR

This paper provides an elementary proof for a nonterminating hypergeometric series summation formula by Gasper and Rahman, and also rederives a related $_3F_2$ identity conjectured by Gosper, using the modified Abel lemma.

Contribution

It introduces a new elementary proof technique for a complex hypergeometric series evaluation and rederives a related conjecture, expanding understanding of these series.

Findings

Elementary proof of Gasper and Rahman's hypergeometric sum

Re-derivation of Gosper's $_3F_2$ conjecture

Enhanced understanding of nonterminating hypergeometric series

Abstract

An elementary proof is given for a nonterminating "strange" cubic $_7F_6$-series summation formula of Gasper and Rahman, through the modified Abel lemma on summation by parts. As a byproduct, an interesting nonterminating $_3F_2({3}/{4})$-series identity conjectured by Gosper, is also rederived.