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arXiv · 2302.14199

On ${}_5ψ_5$ identities of Bailey

Aritram Dhar
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Abstract

In this paper, we provide proofs of two ${}_5ψ_5$ summation formulas of Bailey using a ${}_5ϕ_4$ identity of Carlitz. We show that in the limiting case, the two ${}_5ψ_5$ identities give rise to two ${}_3ψ_3$ summation formulas of Bailey. Finally, we prove the two ${}_3ψ_3$ identities using a technique initially used by Ismail to prove Ramanujan's ${}_1ψ_1$ summation formula and later by Ismail and Askey to prove Bailey's very-well-poised ${}_6ψ_6$ sum.

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Aritram Dhar. 2025-05-04. On ${}_5ψ_5$ identities of Bailey. https://arxiv.org/abs/2302.14199

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