The para-Racah polynomials

2015/11/16 by Jean-Michel Lemay, Lemay, Jean-Michel, Luc Vinet +3 · 1 citation
Mathematics · Physics and Astronomy · #Mathematical functions and polynomials #Optical and Acousto-Optic Technologies #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.1511.05215

Abstract

New bispectral polynomials orthogonal on a quadratic bi-lattice are obtained from a truncation of Wilson polynomials. Recurrence relation and difference equation are provided. The recurrence coefficients can be encoded in a perturbed persymmetric Jacobi matrix. The orthogonality relation and an explicit expression in terms of hypergeometric functions are also given. Special cases and connections with the para-Krawtchouk polynomials and the dual-Hahn polynomials are also discussed.

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