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arXiv · 2108.03858

Charting the $q$-Askey scheme

Tom H. Koornwinder
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Abstract

Following Verde-Star, Linear Algebra Appl. 627 (2021), we label families of orthogonal polynomials in the $q$-Askey scheme together with their $q$-hypergeometric representations by three sequences $x_k, h_k, g_k$ of Laurent polynomials in $q^k$, two of degree 1 and one of degree 2, satisfying certain constraints. This gives rise to a precise classification and parametrization of these families together with their limit transitions. This is displayed in a graphical scheme. We also describe the four-manifold structure underlying the scheme.

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Tom H. Koornwinder. 2021-08-09. Charting the $q$-Askey scheme. https://doi.org/10.1090/conm%2F780%2F15688

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