2022•arXiv (Cornell University)Open access

Orthogonal Polynomials of Askey-Wilson Type

Mourad E. H. Ismail, Ruiming Zhang, Keru Zhou

Abstract

We study two families of orthogonal polynomials. The first is a finite family related to the Askey-Wilson polynomials but the orthogonality is on the real line. A limiting case of this family is an infinite system of orthogonal polynomials whose moment problem is indeterminate. We provide several orthogonality measures for the infinite family and derive their Plancherel-Rotach asymptotics.

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Key concepts: Orthogonal polynomials, Orthogonality, Askey–Wilson polynomials, Hahn polynomials, Discrete orthogonal polynomials, Wilson polynomials, Mathematics, Classical orthogonal polynomials