A new identity for the sum of products of generalized basic hypergeometric functions
arXiv:2009.14694
Abstract
We prove a duality relation for generalized basic hypergeometric functions. It forms a -extension of a recent result of the second and the third named authors and generalizes both a -hypergeometric identity due to the third named author (jointly with Feng and Yang) and a recent identity for the Heine's 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.
17 pages; no figures; as compared to the previous version the paper has more than doubled in size. Main result generalized, three new propositions added, many examples added