A relativistic hypergeometric function
type: Item
instance of: scholarly article
title: A relativistic hypergeometric function
zbMATH Open document ID: 1077.33001
published in: Journal of Computational and Applied Mathematics
publication date: 2005-04-18T00:00:00Z
review text: This paper is a survey of the author's work on a function generalizing the function \({}_2F_1\). This function is a joint eigenfunction of four Askey-Wilson-type hyperbolic difference operators, reducing to the Askey-Wilson polynomials for certain discrete values of the variables. It is defined by a contour integral generalizing the Barnes representation of \({}_2F_1\). It has various symmetries, including a hidden \(D_4\) symmetry in the parameters. By means of the associated Hilbert space transform, the difference operators can be promoted to self-adjoint operators, provided the parameters vary over a certain polytope in the parameter space \(\Pi\). For a dense subset of \(\Pi\), parameter shifts give rise to an explicit evaluation in terms of rational functions of exponentials.
Mathematics Subject Classification ID: 33-02
Mathematics Subject Classification ID: 33D99
Mathematics Subject Classification ID: 39A70
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 46N50
Mathematics Subject Classification ID: 81U15
zbMATH DE Number: 2157682
zbMATH Keywords: generalized hypergeometric function
zbMATH Keywords: Askey-Wilson difference operators
zbMATH Keywords: Askey-Wilson polynomials
zbMATH Keywords: Hilbert space transform
zbMATH Keywords: parameter shifts
author: Simon Ruijsenaars
reviewed by: José L. López
MaRDI profile type: Publication
full work available at URL: j.cam.2004.05.024
OpenAlex ID: W2110600073
cites work: Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
cites work: Q4222737
cites work: Q5289118
cites work: Q4040884
cites work: Some functions that generalize the Askey-Wilson polynomials
cites work: Askey-Wilson type functions with bound states
cites work: The Associated Askey-Wilson Polynomials
cites work: The Askey-Wilson function transform
cites work: First order analytic difference equations and integrable quantum systems
cites work: Hilbert-Schmidt operators vs. integrable systems of elliptic Calogero-Moser type. I: The eigenfunction identities
cites work: A generalized hypergeometric function satisfying four analytic difference equations of Askey-Wilson type
cites work: Special functions associated with Calogero-Moser type quantum systems
cites work: Hilbert space theory for reflectionless relativistic potentials
cites work: Special functions defined by analytic difference equations
cites work: Sine-Gordon solitons vs. relativistic Calogero-Moser particles
cites work: Relativistic Lamé functions revisited.
cites work: A generalized hypergeometric function. II: Asymptotics and \(D_4\) symmetry
cites work: A generalized hypergeometric function. III: Associated Hilbert space transform
cites work: Relativistic Lamé functions: Completeness vs. polynomial asymptotics
cites work: Parameter shifts,D4symmetry and joint eigenfunctions for commuting Askey–Wilson-type difference operators
cites work: Q4657351
cites work: Askey-Wilson Functions and Quantum Groups
cites work: Hyperbolic beta integrals
cites work: Some orthogonal very-well-poised \(_8\varphi_7\)-functions that generalize Askey-Wilson polynomials
cites work: Q3844537
DOI: 10.1016/J.CAM.2004.05.024
Recommended article: Q4698295
Recommended article: A relativistic variant of the Wigner function
Recommended article: Relativistic jacobi polynomials
Recommended article: Hypergeometric equation in modeling relativistic isotropic sphere
Recommended article: The relativistic szegö polynomials
Recommended article: Q3155590
Recommended article: Q4893904
Recommended article: Q4470217
Recommended article: Relativistic spherical functions on the Lorentz group
description: scientific article; zbMATH DE number 2157682