{
  "id": "2006.15236",
  "version": "v1",
  "published": "2020-06-26T23:03:50.000Z",
  "updated": "2020-06-26T23:03:50.000Z",
  "title": "Orthogonal polynomials and Hankel Determinants for certain Bernoulli and Euler Polynomials",
  "authors": [
    "Karl Dilcher",
    "Lin Jiu"
  ],
  "categories": [
    "math.NT",
    "math.CA",
    "math.CV"
  ],
  "abstract": "Using continued fraction expansions of certain polygamma functions as a main tool, we find orthogonal polynomials with respect to the odd-index Bernoulli polynomials $B_{2k+1}(x)$ and the Euler polynomials $E_{2k+\\nu}(x)$, for $\\nu=0, 1, 2$. In the process we also determine the corresponding Jacobi continued fractions (or J-fractions) and Hankel determinants. In all these cases the Hankel determinants are polynomials in $x$ which factor completely over the rationals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-26T23:03:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B68",
      "33D45",
      "11C20",
      "30B70"
    ],
    "keywords": [
      "hankel determinants",
      "euler polynomials",
      "orthogonal polynomials",
      "odd-index bernoulli polynomials",
      "polygamma functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}