On Summations of Generalized Hypergeometric Functions with Integral Parameter Differences

Kirill Bakhtin and Elena Prilepkina ()
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Kirill Bakhtin: Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok 690041, Russia
Elena Prilepkina: Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok 690041, Russia

Mathematics, 2024, vol. 12, issue 11, 1-17

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.

Keywords: generalized hypergeometric function; summation formulas; hypergeometric identity; Miller–Paris transformations; Euler–Pfaff type transformations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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