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On 5ψ5 identities of Bailey

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

    In this paper, we provide proofs of two 5ψ5 summation formulas of Bailey using a 5ϕ4 identity of Carlitz. We show that in the limiting case, the two 5ψ5 identities give rise to two 3ψ3 summation formulas of Bailey. Finally, we prove the two 3ψ3 identities using a technique initially used by Ismail to prove Ramanujan’s 1ψ1 summation formula and later by Ismail and Askey to prove Bailey’s very-well-poised 6ψ6 sum.

    AMSC: 33D15, 33D65
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