Tridiagonalization of the hypergeometric operator and the Racah–Wilson algebra
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- by Vincent X. Genest, Mourad E. H. Ismail, Luc Vinet and Alexei Zhedanov PDF
- Proc. Amer. Math. Soc. 144 (2016), 4441-4454 Request permission
Abstract:
The algebraic underpinning of the tridiagonalization procedure is investigated. The focus is put on the tridiagonalization of the hypergeometric operator and its associated quadratic Jacobi algebra. It is shown that under tridiagonalization, the quadratic Jacobi algebra becomes the quadratic Racah–Wilson algebra associated to the generic Racah–Wilson polynomials. A degenerate case leading to the Hahn algebra is also discussed.References
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Additional Information
- Vincent X. Genest
- Affiliation: Centre de Recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal, Québec H3C 3J7 Canada
- Address at time of publication: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139
- MR Author ID: 970414
- Email: vxgenest@mit.edu
- Mourad E. H. Ismail
- Affiliation: Department of Mathematics, King Saud University, Riyadh, Saudi Arabia–and– Department of Mathematics, University of Central Florida, Orlando, Florida 32816
- MR Author ID: 91855
- Email: mourad.eh.ismail@gmail.com
- Luc Vinet
- Affiliation: Centre de Recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal, Québec H3C 3J7 Canada
- MR Author ID: 178665
- ORCID: 0000-0001-6211-7907
- Email: vinetl@crm.umontreal.ca
- Alexei Zhedanov
- Affiliation: Centre de Recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal, Québec H3C 3J7 Canada
- MR Author ID: 234560
- Email: zhedanov@yahoo.com
- Received by editor(s): June 25, 2015
- Received by editor(s) in revised form: December 29, 2015
- Published electronically: April 27, 2016
- Communicated by: Walter Van Assche
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4441-4454
- MSC (2010): Primary 33C45, 33C80, 42C05
- DOI: https://doi.org/10.1090/proc/13082
- MathSciNet review: 3531193