{
  "id": "2108.07517",
  "version": "v1",
  "published": "2021-08-17T09:03:48.000Z",
  "updated": "2021-08-17T09:03:48.000Z",
  "title": "Zeros of quasi-orthogonal $q$-Laguerre polynomials",
  "authors": [
    "Pinaki Prasad Kar",
    "Priyabrat Gochhayat"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We investigate the interlacing of zeros of polynomials of different degrees within the sequences of $q$-Laguerre polynomials $\\left\\{\\tilde{L}_n^{(\\delta)}(z;q)\\right\\}_{n=0}^{\\infty}$ characterized by $\\delta\\in(-2,-1).$ The interlacing of zeros of quasi-orthogonal polynomials $\\tilde{L}_n^{(\\delta)}(z;q)$ with those of the orthogonal polynomials $\\tilde{L}_m^{(\\delta+t)}(z;q), m,n\\in\\mathbb{N}, t\\in\\{1,2\\}$ is also considered. New bounds for the least zero of the (order $1$) quasi-orthogonal $q$-Laguerre polynomials are derived.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-17T09:03:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D15",
      "33D45"
    ],
    "keywords": [
      "laguerre polynomials",
      "quasi-orthogonal polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}