{
  "id": "0812.0730",
  "version": "v1",
  "published": "2008-12-03T14:38:42.000Z",
  "updated": "2008-12-03T14:38:42.000Z",
  "title": "Zeros of linear combinations of Laguerre polynomials from different sequences",
  "authors": [
    "K Driver",
    "K Jordaan"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely $R_n=L_n^{\\alpha}+aL_{n}^{\\alpha'}$ and $S_n=L_n^{\\alpha}+bL_{n-1}^{\\alpha'}$. Proofs and numerical counterexamples are given in situations where the zeros of $R_n$, and $S_n$, respectively, interlace (or do not in general) with the zeros of $L_k^{\\alpha}$, $L_k^{\\alpha'}$, $k=n$ or $n-1$. The results we prove hold for continuous, as well as integral, shifts of the parameter $\\alpha$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-03T14:38:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45",
      "42C05"
    ],
    "keywords": [
      "linear combinations",
      "laguerre polynomials",
      "study interlacing properties",
      "numerical counterexamples",
      "situations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.cam.2009.02.091",
      "journal": "Journal of Computational and Applied Mathematics",
      "year": 2009,
      "month": "Dec",
      "volume": 233,
      "number": 3,
      "pages": 719
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JCoAM.233..719D"
    }
  }
}