Diophantine properties of orthogonal polynomials and rational functions
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- by Mourad E. H. Ismail and Mizan Rahman PDF
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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.References
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Additional Information
- Mourad E. H. Ismail
- Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
- MR Author ID: 91855
- Email: mourad.eh.ismail@gmail.com
- Mizan Rahman
- Affiliation: Deceased, formerly Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada
- Received by editor(s): June 9, 2013
- Received by editor(s) in revised form: September 6, 2013
- Published electronically: February 20, 2017
- Additional Notes: This research was supported by Research Grants Council of Hong Kong under contract #101411
- Communicated by: Walter Van Assche
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 2427-2440
- MSC (2010): Primary 33C20; Secondary 33C45
- DOI: https://doi.org/10.1090/proc/12355
- MathSciNet review: 3626501