{
  "id": "2305.06623",
  "version": "v1",
  "published": "2023-05-11T07:42:10.000Z",
  "updated": "2023-05-11T07:42:10.000Z",
  "title": "Hankel determinants and Jacobi continued fractions for $q$-Euler numbers",
  "authors": [
    "Lin Jiu",
    "Shane Chern"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "The $q$-analogs of Bernoulli and Euler numbers were introduced by Carlitz. Similar to the recent results on the Hankel determinants for the $q$-Bernoulli numbers established by Chapoton and Zeng, we determine parallel evaluations for the $q$-Euler numbers. It is shown that the associated Favard-type orthogonal polynomials for $q$-Euler numbers are given by a specialization of the big $q$-Jacobi polynomials, thereby leading to their corresponding Jacobi continued fraction expression, which eventually serves as a key to our determinant evaluations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-11T07:42:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B68",
      "11C20",
      "30B70",
      "33D45"
    ],
    "keywords": [
      "euler numbers",
      "hankel determinants",
      "determine parallel evaluations",
      "corresponding jacobi continued fraction expression",
      "associated favard-type orthogonal polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}