{
  "id": "1507.01622",
  "version": "v1",
  "published": "2015-07-06T20:57:23.000Z",
  "updated": "2015-07-06T20:57:23.000Z",
  "title": "Zeros of polynomials orthogonal with respect to a signed weight",
  "authors": [
    "M. Benabdallah",
    "M. J. Atia",
    "R. S. Costas-Santos"
  ],
  "comment": "12 pages, 1 figure",
  "journal": "Indag. Math. (N.S.) 23 (2012), no. 1-2, 26-31",
  "doi": "10.1016/j.cam.2008.07.055",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper we consider the polynomial sequence $(P_{n}^{\\alpha,q}(x))$ that is orthogonal on $[-1,1]$ with respect to the weight function $x^{2q+1}(1-x^{2})^{\\alpha}(1-x), \\alpha>-1, q\\in \\mathbb N$; we obtain the coefficients of the tree-term recurrence relation (TTRR) by using a different method from the one derived in \\cite{kn:atia1}; we prove that the interlacing property does not hold properly for $(P_n^{\\alpha,q}(x))$; and we also prove that, if $x_{n,n}^{\\alpha+i,q+j}$ is the largest zero of $P_{n}^{\\alpha+i,q+j}(x)$, $\\displaystyle x_{2n-2j,2n-2j}^{\\alpha+j,q+j}< x_{2n-2i,2n-2i}^{\\alpha+i,q+i}, 0\\leq i<j\\leq n-1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-06T20:57:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C05",
      "33C20",
      "42C05",
      "30C15"
    ],
    "keywords": [
      "polynomials orthogonal",
      "signed weight",
      "tree-term recurrence relation",
      "weight function",
      "largest zero"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Journal of Computational and Applied Mathematics",
      "year": 2009,
      "month": "Mar",
      "volume": 225,
      "number": 2,
      "pages": 440
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JCoAM.225..440C"
    }
  }
}