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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Veröffentlicht in:Mathematics (Basel) Jg. 12; H. 11; S. 1656
Hauptverfasser: Bakhtin, Kirill, Prilepkina, Elena
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.06.2024
Schlagworte:
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
Russia
ISSN:2227-7390, 2227-7390
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:2227-7390
2227-7390
DOI:10.3390/math12111656