On 5ψ5 Identities of Bailey

Abstract

A BSTRACT . In this paper, we provide proofs of two 5 ψ 5 summation formulas of Bailey using a 5 φ 4 identity of Carlitz. We show that in the limiting case, the two 5 ψ 5 identities give rise to two 3 ψ 3 summation formulas of Bailey. Finally, we prove the two 3 ψ 3 identities using a technique initially used by Ismail to prove Ramanujan’s 1 ψ 1 summation formula and later by Ismail and Askey to prove Bailey’s very-well-poised 6 ψ 6 sum.