Bispectrality of Meixner type polynomials
Meixner type polynomials are defined from the Meixner polynomials by using Casoratian determinants whose entries belong to two given finite sets of polynomials and . They are eigenfunctions of higher order difference operators but only for a careful choice of the polynomials and , the sequence is or...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2021 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/182276 |
| Acesso em linha: | https://hdl.handle.net/11441/182276 https://doi.org/10.1016/j.jat.2020.105521 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Orthogonal polynomials Bispectral orthogonal polynomials Recurrence relations Algebra of difference operators Meixner polynomials |
| Resumo: | Meixner type polynomials are defined from the Meixner polynomials by using Casoratian determinants whose entries belong to two given finite sets of polynomials and . They are eigenfunctions of higher order difference operators but only for a careful choice of the polynomials and , the sequence is orthogonal with respect to a measure. In this paper, we prove that the Meixner type polynomials always satisfy higher order recurrence relations (hence, they are bispectral). We also introduce and characterize the algebra of difference operators associated to these recurrence relations. Our characterization is constructive and surprisingly simple. As a consequence, we determine the unique choice of the polynomials and such that the sequence is orthogonal with respect to a measure. |
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