Exceptional Jacobi polynomials which are deformations of Jacobi polynomials

In [10] we constructed new examples of exceptional Jacobi polynomials. The difference with the so called standard families is that the examples constructed in [10] depend on an arbitrary number of continuous parameters. Besides these continuous parameters, denoted by M = {Mo M1,...}, each one of the...

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Detalles Bibliográficos
Autor: Durán Guardeño, Antonio José
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/182367
Acceso en línea:https://hdl.handle.net/11441/182367
https://doi.org/10.1016/j.jmaa.2023.127523
Access Level:acceso abierto
Palabra clave:Orthogonal polynomials
Jacobi polynomials
Exceptional orthogonal polynomials
Exceptional Jacobi polynomials
Descripción
Sumario:In [10] we constructed new examples of exceptional Jacobi polynomials. The difference with the so called standard families is that the examples constructed in [10] depend on an arbitrary number of continuous parameters. Besides these continuous parameters, denoted by M = {Mo M1,...}, each one of the new families of exceptional Jacobi polynomials is associated to two negative integers a < b < -1 and a finite set of positive integers F satisfying that {-b,...,-a -b -1} C F. In this paper we prove that when F = {u,u+1,..., -a -b -1}, with 1 < u < -b, the exceptional Jacobi polynomials are deformations of Jacobi polynomials (when the continuous parameters Mi -- 1. Otherwise, the exceptional Jacobi polynomials are deformations of standard exceptional Jacobi polynomials (again when the continuous parameters Mi --1).