Charting the $q$-Askey scheme
Classical Analysis and ODEs
2022-09-07 v2
Abstract
Following Verde-Star, Linear Algebra Appl. 627 (2021), we label families of orthogonal polynomials in the -Askey scheme together with their -hypergeometric representations by three sequences of Laurent polynomials in , 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.
Cite
@article{arxiv.2108.03858,
title = {Charting the $q$-Askey scheme},
author = {Tom H. Koornwinder},
journal= {arXiv preprint arXiv:2108.03858},
year = {2022}
}
Comments
17 pages, one figure; in v2 minor corrections, one remark and three references added; to appear in "Proceedings of the Conference on Hypergeometry, Integrability and Lie Theory", Contemporary Mathematics