{
  "id": "2002.01518",
  "version": "v1",
  "published": "2020-02-04T19:47:28.000Z",
  "updated": "2020-02-04T19:47:28.000Z",
  "title": "Combinatorial formulas for the coefficients of the Al-Salam-Chihara polynomials",
  "authors": [
    "Donghyun Kim"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The Al-Salam-Chihara polynomials are an important family of orthogonal polynomials in one variable $x$ depending on 3 parameters $\\alpha$, $\\beta$ and $q$. They are closely connected to a model from statistical mechanics called the partially asymmetric simple exclusion process (PASEP) and they can be obtained as a specialization of the Askey-Wilson polynomials. We give two different combinatorial formulas for the coefficients of the (transformed) Al-Salam-Chihara polynomials. Our formulas make manifest the fact that the coefficients are polynomials in $\\alpha$, $\\beta$ and $q$ with positive coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-04T19:47:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "al-salam-chihara polynomials",
      "combinatorial formulas",
      "coefficients",
      "partially asymmetric simple exclusion process",
      "orthogonal polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}