<Reference List> | |
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 |