Diophantine Properties Of Orthogonal Polynomials And Rational Functions

Keywords

Associated Askey-Wilson polynomials; Associated Wilson polynomials; Biorthogonal rational functions; Contiguous relations; Factorization; Isochronous systems; R functions II

Abstract

Calogero and his collaborators recently observed that some hypergeometric polynomials can be factored as a product of two polynomials, one of which is factored into a product of linear terms. Chen and Ismail showed that this property prevails through all polynomials in the Askey scheme. We show that this factorization property is also shared by the associated Wilson and Askey-Wilson polynomials and some biorthogonal rational functions. This is applied to a specific model of an isochronous system of particles with small oscillations around the equilibrium position.

Publication Date

1-1-2017

Publication Title

Proceedings of the American Mathematical Society

Volume

145

Issue

6

Number of Pages

2427-2440

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/proc/12355

Socpus ID

85016221950 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85016221950

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