On Summations of Generalized Hypergeometric Functions with Integral Parameter Differences

Autor:	Kirill Bakhtin, Elena Prilepkina
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	generalized hypergeometric function summation formulas hypergeometric identity Miller–Paris transformations Euler–Pfaff type transformations Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 11, p 1656 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12111656
Popis:	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.
Databáze:	Directory of Open Access Journals
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