Diophantine properties of orthogonal polynomials and rational functions
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.
|Keywords||Associated Askey-Wilson polynomials, Associated Wilson polynomials, Biorthogonal rational functions, Contiguous relations, Factorization, Isochronous systems, RII functions|
|Journal||Proceedings of the American Mathematical Society|
Ismail, M.E.H. (Mourad E. H.), & Rahman, M. (Mizan). (2017). Diophantine properties of orthogonal polynomials and rational functions. Proceedings of the American Mathematical Society, 145(6), 2427–2440. doi:10.1090/proc/12355