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Mathematics > Classical Analysis and ODEs

arXiv:2009.14694 (math)
[Submitted on 30 Sep 2020 (v1), last revised 7 Sep 2021 (this version, v2)]

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

Authors:S.I.Kalmykov, D.Karp, A.Kuznetsov
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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 ${}_2\phi_{1}$ 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.
Comments: 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
Subjects: Classical Analysis and ODEs (math.CA)
MSC classes: 33D15
Cite as: arXiv:2009.14694 [math.CA]
  (or arXiv:2009.14694v2 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.2009.14694

Submission history

From: Dmitrii B. Karp [view email]
[v1] Wed, 30 Sep 2020 14:18:03 UTC (12 KB)
[v2] Tue, 7 Sep 2021 22:21:08 UTC (13 KB)
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