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The algebra of recurrence relations for exceptional Laguerre and Jacobi polynomials


Author: Antonio J. Durán
Journal: Proc. Amer. Math. Soc. 149 (2021), 173-188
MSC (2010): Primary 42C05, 33C45, 33E30
DOI: https://doi.org/10.1090/proc/15267
Published electronically: October 9, 2020
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Abstract: Exceptional Laguerre and Jacobi polynomials $ p_n(x)$ are bispectral, in the sense that as functions of the continuous variable $ x$, they are eigenfunctions of a second order differential operator and as functions of the discrete variable $ n$, they are eigenfunctions of a higher order difference operator (the one defined by any of the recurrence relations they satisfy). In this paper, under mild conditions on the sets of parameters, we characterize the algebra of difference operators associated to the higher order recurrence relations satisfied by the exceptional Laguerre and Jacobi polynomials.


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Additional Information

Antonio J. Durán
Affiliation: Departamento de Análisis Matemático, Universidad de Sevilla, Apdo (P. O. Box) 1160, 41080 Sevilla, Spain
Email: duran@us.es

DOI: https://doi.org/10.1090/proc/15267
Keywords: Laguerre exceptional polynomials, Jacobi exceptional polynomials, recurrence relations
Received by editor(s): February 25, 2020
Received by editor(s) in revised form: July 8, 2020
Published electronically: October 9, 2020
Additional Notes: The author was partially supported by PGC2018-096504-B-C31 (FEDER(EU)/Ministerio de Ciencia e Innovación-Agencia Estatal de Investigación), FQM-262, and Feder-US-1254600 (FEDET(EU)/Junta de Andalucía).
Communicated by: Mourad E. H. Ismail
Article copyright: © Copyright 2020 American Mathematical Society