On Summations of Generalized Hypergeometric Functions with Integral Parameter Differences
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 whic...
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| Vydáno v: | Mathematics (Basel) Ročník 12; číslo 11; s. 1656 |
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| Jazyk: | angličtina |
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01.06.2024
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| 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 F34. 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. |
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| AbstractList | 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 F34. 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. |
| Audience | Academic |
| Author | Bakhtin, Kirill Prilepkina, Elena |
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| Cites_doi | 10.1063/1.1665587 10.1007/s10092-018-0272-5 10.1216/RMJ-2013-43-1-291 10.1017/CBO9781107325937 10.1063/1.531222 10.1080/10652469.2018.1526793 10.3390/math8111966 10.1007/978-1-4757-3675-5_20 10.3390/sym14081541 10.1137/0512020 10.1063/1.1665270 10.1134/S1995080222090128 10.37394/23206.2022.21.69 10.1142/0270 10.1007/1-4020-2634-X_17 10.1134/S1995080220050029 10.1016/j.jat.2020.105484 10.3390/sym13101783 10.1007/s00029-003-0310-1 10.1063/1.530536 |
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| References | Kanemitsu (ref_6) 2002; Volume 8 Chu (ref_17) 1995; 36 Schlosser (ref_18) 2003; 9 ref_11 ref_22 ref_10 Minton (ref_13) 1970; 12 ref_21 Candezano (ref_23) 2020; 41 ref_1 Miller (ref_24) 2013; 43 ref_3 Karlsson (ref_14) 1971; 12 Chu (ref_16) 1994; 35 ref_2 ref_19 Lima (ref_20) 2020; 260 Quintana (ref_7) 2018; 55 Cesarano (ref_8) 2022; 21 Gasper (ref_15) 1981; 12 Karp (ref_9) 2018; 29 Karp (ref_12) 2022; 43 ref_5 ref_4 |
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| SubjectTerms | Distributions, Theory of (Functional analysis) Euler–Pfaff type transformations Functions, Hypergeometric generalized hypergeometric function Hypergeometric functions hypergeometric identity Integrals Mathematical research Methods Miller–Paris transformations Parameter estimation Parameters summation formulas |
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| Title | On Summations of Generalized Hypergeometric Functions with Integral Parameter Differences |
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