2015•arXiv (Cornell University)Open access

The para-Racah polynomials

Jean-Michel Lemay, Luc Vinet, Alexei Zhedanov

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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Key concepts: Wilson polynomials, Hahn polynomials, Orthogonal polynomials, Kravchuk polynomials, Discrete orthogonal polynomials, Classical orthogonal polynomials, Mathematics, Jacobi polynomials