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On Summations of Generalized Hypergeometric Functions with Integral Parameter Differences

Author

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  • Kirill Bakhtin

    (Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok 690041, Russia
    Institute of Applied Mathematics, Far Eastern Federal University, Vladivostok 690950, Russia
    These authors contributed equally to this work.)

  • Elena Prilepkina

    (Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok 690041, Russia
    These authors contributed equally to this work.)

Abstract

In this paper, we present an extension of the Karlsson–Minton summation formula for a generalized hypergeometric function with integral parameter differences. Namely, we extend one single negative difference in Karlsson–Minton formula to a finite number of integral negative differences, some of which will be repeated. Next, we continue our study of the generalized hypergeometric function evaluated at unity and with integral positive differences (IPD hypergeometric function at the unit argument). We obtain a recurrence relation that reduces the IPD hypergeometric function at the unit argument to F 3 4 . Finally, we note that Euler–Pfaff-type transformations are always based on summation formulas for finite hypergeometric functions, and we give a number of examples.

Suggested Citation

  • Kirill Bakhtin & Elena Prilepkina, 2024. "On Summations of Generalized Hypergeometric Functions with Integral Parameter Differences," Mathematics, MDPI, vol. 12(11), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1656-:d:1401670
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