{
  "abstract": "We present a determinantal evaluation formula for the very-well-poised ${}_8Φ_7$ basic hypergeometric Askey-Wilson function in terms of elementary functions. The formula in question is valid for discrete values of the four permutation-symmetric Askey-Wilson parameters; specifically, these consist of all quadruples of parameter values that are given, up to a sign, by powers $q^k$ with $k$ a positive integer or half-integer, in such a way that each of the four types (positive/negative sign, integer/half-integer power) occurs exactly once. The proof hinges on a product formula for an associated Cauchy-type determinant, which is of independent interest and is established here by elementary means using Krattenthaler's `identification of factors' method for determinant evaluations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37390",
  "author_total": 2,
  "authors": [
    {
      "name": "J. F. van Diejen"
    },
    {
      "name": "A. N. Kirillov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/474ppgj3kp57z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37390",
  "fulltext_url": null,
  "id": "474ppgj3kp57z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37390",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7214992521",
  "pdf_url": "https://arxiv.org/pdf/2609.37390",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/474ppgj3kp57z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.37390",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37390"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Elementary Askey-Wilson Functions",
  "title_text": "Elementary Askey-Wilson Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/474ppgj3kp57z",
  "venue": "arXiv",
  "versions": []
}