On classical orthogonal polynomials on bi-lattices
Classical Analysis and ODEs
2025-02-06 v2
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.
Cite
@article{arxiv.2311.05636,
title = {On classical orthogonal polynomials on bi-lattices},
author = {K. Castillo and G. Filipuk and D. Mbouna},
journal= {arXiv preprint arXiv:2311.05636},
year = {2025}
}