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arXiv · 2311.05636

On classical orthogonal polynomials on bi-lattices

K. Castillo·G. Filipuk·D. Mbouna
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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.

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K. Castillo, G. Filipuk, D. Mbouna. 2023-10-26. On classical orthogonal polynomials on bi-lattices. https://arxiv.org/abs/2311.05636

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