Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, vol.17, 2021 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 17
- Publication Date: 2021
- Doi Number: 10.3842/sigma.2021.098
- Journal Name: SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
- Open Archive Collection: AVESIS Open Access Collection
- Istanbul Kültür University Affiliated: Yes
Abstract
The main goal of this paper is to derive a number of identities for the generalized hypergeometric function evaluated at unity and for certain terminating multivariate hyper-geometric functions from the symmetries and other properties of Meijer's G function. For instance, we recover two- and three-term Thomae relations for F-3(2), give two- and three-term transformations for F-4(3) with one unit shift and F-5(4) with two unit shifts in the parameters, establish multi-term identities for general F-p(p-1) and several transformations for terminating Kampe de Feriet and Srivastava F-(3) functions. We further present a presumably new formula for analytic continuation of F-p(p-1)(1) in parameters and reveal somewhat unexpected connections between the generalized hypergeometric functions and the generalized and ordinary Bernoulli polynomials. Finally, we exploit some recent duality relations for the generalized hypergeometric and q-hypergeometric functions to derive multi-term relations for terminating series.