{
  "id": "2412.06844",
  "version": "v1",
  "published": "2024-12-07T18:20:15.000Z",
  "updated": "2024-12-07T18:20:15.000Z",
  "title": "Interlacing of zeros from different sequences of Meixner-Pollaczek, Pseudo-Jacobi and Continuous Hahn polynomials",
  "authors": [
    "Aletta Jooste",
    "Kerstin Jordaan"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper we consider interlacing of the zeros of polynomials from different sequences $\\{p_n\\}$ and $\\{g_n\\}$. In our main result we consider a mixed recurrence equation necessary for existence of a linear term $(x-A)$ so that the $(n+1)$ zeros of $(x-A)g_n(x)$ interlace with the $n$ zeros of $p_n$. We apply our result to Meixner-Pollaczek, Pseudo-Jacobi and Continuous Hahn polynomials to obtain new interlacing results for the zeros of polynomials of the same degree from different polynomial sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-07T18:20:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous hahn polynomials",
      "meixner-pollaczek",
      "pseudo-jacobi",
      "interlacing",
      "mixed recurrence equation necessary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}