A new identity for the sum of products of generalized basic hypergeometric functions

2020/09/30 by S. I. Kalmykov, Kalmykov, S. I., D. Karp +3
Mathematics · #Mathematical functions and polynomials #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2009.14694

Abstract

We prove a duality relation for generalized basic hypergeometric functions. It forms a q-extension of a recent result of the second and the third named authors and generalizes both a q-hypergeometric identity due to the third named author (jointly with Feng and Yang) and a recent identity for the Heine's ₂ϕ₁ function due to Suzuki. We further explore various consequences of our identity leading to several presumably new multi-term relations for both terminating and non-terminating generalized basic hypergeometric series. Moreover, we give confluent versions of our results and furnish a number of explicit examples.

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