{
  "id": "1112.4230",
  "version": "v2",
  "published": "2011-12-19T03:36:00.000Z",
  "updated": "2012-09-28T03:26:36.000Z",
  "title": "Kernel identities for van Diejen's $q$-difference operators and transformation formulas for multiple basic hypergeometric series",
  "authors": [
    "Yasuho Masuda"
  ],
  "comment": "29 pages. Typos corrected. Subsection 4.3 is modified",
  "categories": [
    "math.CA",
    "math.QA"
  ],
  "abstract": "In this paper, we show that the kernel function of Cauchy type for type $BC$ intertwines the commuting family of van Diejen's $q$-difference operators. This result gives rise to a transformation formula for certain multiple basic hypergeometric series of type $BC$. We also construct a new infinite family of commuting $q$-difference operators for which the Koornwinder polynomials are joint eigenfunctions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-28T03:26:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D52",
      "33D67"
    ],
    "keywords": [
      "multiple basic hypergeometric series",
      "difference operators",
      "van diejens",
      "transformation formula",
      "kernel identities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.4230M"
    }
  }
}