Research PaperNo Access

On $_{5} ψ_{5}$ identities of Bailey

Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, FL 32611, USA

https://doi.org/10.1142/S179304212450026XCited by:0 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 33D15, 33D65

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