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

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Abstract

We prove a duality relation for the 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.

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Acknowledgements

We thank the anonymous referees for a number of useful suggestions that led to a substantial improvement of this paper. The research of A. K. was supported by the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dongchuan Rd., Shanghai, 200240, China

    S. I. Kalmykov

  2. Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia

    S. I. Kalmykov

  3. Department of Mathematics, Holon Institute of Technology, 52 Golomb Street, POB 305, 5810201, Holon, Israel

    D. Karp

  4. Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada

    A. Kuznetsov

Authors
  1. S. I. Kalmykov
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  2. D. Karp
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  3. A. Kuznetsov
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Correspondence to D. Karp.

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To the memory of Richard Askey.

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Kalmykov is supported by NSFC Grant 11901384. The research of A. Kuznetsov is supported by the Natural Sciences and Engineering Research Council of Canada.

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Kalmykov, S.I., Karp, D. & Kuznetsov, A. A new identity for the sum of products of the generalized basic hypergeometric functions. Ramanujan J 61, 391–414 (2023). https://doi.org/10.1007/s11139-022-00598-w

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  • DOI: https://doi.org/10.1007/s11139-022-00598-w

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