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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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/182367 |
| Acesso em linha: | https://hdl.handle.net/11441/182367 https://doi.org/10.1016/j.jmaa.2023.127523 |
| Access Level: | acceso abierto |
| Palavra-chave: | Orthogonal polynomials Jacobi polynomials Exceptional orthogonal polynomials Exceptional Jacobi polynomials |
| Resumo: | 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). |
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