{
  "id": "2108.03858",
  "version": "v1",
  "published": "2021-08-09T07:59:46.000Z",
  "updated": "2021-08-09T07:59:46.000Z",
  "title": "Charting the $q$-Askey scheme",
  "authors": [
    "Tom H. Koornwinder"
  ],
  "comment": "17 pages, one figure",
  "categories": [
    "math.CA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-09T07:59:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D45"
    ],
    "keywords": [
      "askey scheme",
      "linear algebra appl",
      "hypergeometric representations",
      "limit transitions",
      "precise classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}