On classical orthogonal polynomials on bi-lattices (Preprint)

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Type: Preprint
National /International: International
Title: On classical orthogonal polynomials on bi-lattices
Publication Date: 2023-10-26
Authors: - Kenier Castillo
- Galina Filipuk
- Dieudonné Mbouna
Abstract:

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.

Institution: arXiv:2311.05636
Online version: https://arxiv.org/abs/2311.05636
Download: Not available
 
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