Certain Generalizations of Quadratic Transformations of Hypergeometric and Generalized Hypergeometric Functions

Autor: Mohd Idris Qureshi, Junesang Choi, Tafaz Rahman Shah
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Symmetry, Vol 14, Iss 5, p 1073 (2022)
Druh dokumentu: article
ISSN: 2073-8994
DOI: 10.3390/sym14051073
Popis: There have been numerous investigations on the hypergeometric series 2F1 and the generalized hypergeometric series pFq such as differential equations, integral representations, analytic continuations, asymptotic expansions, reduction cases, extensions of one and several variables, continued fractions, Riemann’s equation, group of the hypergeometric equation, summation, and transformation formulae. Among the various approaches to these functions, the transformation formulae for the hypergeometric series 2F1 and the generalized hypergeometric series pFq are significant, both in terms of applications and theory. The purpose of this paper is to establish a number of transformation formulae for pFq, whose particular cases would include Gauss’s and Kummer’s quadratic transformation formulae for 2F1, as well as their two extensions for 3F2, by making advantageous use of a recently introduced sequence and some techniques commonly used in dealing with pFq theory. The pFq function, which is the most significant function investigated in this study, exhibits natural symmetry.
Databáze: Directory of Open Access Journals
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