On classical orthogonal polynomials on bi-lattices
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913678196998144 |
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| author | Castillo, K. Filipuk, G. Mbouna, D. |
| author_facet | Castillo, K. Filipuk, G. Mbouna, D. |
| contents | In [J. Phys. A: Math. Theor. 45 (2012)], while looking for spin chains that admit perfect state transfer, Vinet and Zhedanov found an apparently new sequence of orthogonal polynomials, that they called para-Krawtchouk polynomials, defined on a bilinear lattice. In this note we present necessary and sufficient conditions for the regularity of solutions of the corresponding functional equation. Moreover, the functional Rodrigues formula and a closed formula for the recurrence coefficients are presented. As a consequence, we characterize all solutions of the functional equation, including as very particular cases the Meixner, Charlier, Krawtchouk, Hahn, and para-Krawtchouk polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05636 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On classical orthogonal polynomials on bi-lattices Castillo, K. Filipuk, G. Mbouna, D. Classical Analysis and ODEs 42C05, 33C45 In [J. Phys. A: Math. Theor. 45 (2012)], while looking for spin chains that admit perfect state transfer, Vinet and Zhedanov found an apparently new sequence of orthogonal polynomials, that they called para-Krawtchouk polynomials, defined on a bilinear lattice. In this note we present necessary and sufficient conditions for the regularity of solutions of the corresponding functional equation. Moreover, the functional Rodrigues formula and a closed formula for the recurrence coefficients are presented. As a consequence, we characterize all solutions of the functional equation, including as very particular cases the Meixner, Charlier, Krawtchouk, Hahn, and para-Krawtchouk polynomials. |
| title | On classical orthogonal polynomials on bi-lattices |
| topic | Classical Analysis and ODEs 42C05, 33C45 |
| url | https://arxiv.org/abs/2311.05636 |