{
  "id": "1210.0207",
  "version": "v2",
  "published": "2012-09-30T14:48:41.000Z",
  "updated": "2013-03-06T14:39:33.000Z",
  "title": "Confluence of apparent singularities in multi-indexed orthogonal polynomials: the Jacobi case",
  "authors": [
    "C. -L. Ho",
    "R. Sasaki",
    "K. Takemura"
  ],
  "comment": "27 pages, no figures. A Table added to summarize the main results, typos corrected, some statements added to improve presentation. Version in J. Phys. A",
  "journal": "J. Phys. A: Math. Theor. 46 (2013) 115205",
  "categories": [
    "math.CA",
    "hep-th",
    "math-ph",
    "math.MP",
    "nlin.SI",
    "quant-ph"
  ],
  "abstract": "The multi-indexed Jacobi polynomials are the main part of the eigenfunctions of exactly solvable quantum mechanical systems obtained by certain deformations of the P\\\"oschl-Teller potential (Odake-Sasaki). By fine-tuning the parameter(s) of the P\\\"oschl-Teller potential, we obtain several families of explicit and global solutions of certain second order Fuchsian differential equations with an apparent singularity of characteristic exponent -2 and -1. They form orthogonal polynomials over $x\\in(-1,1)$ with weight functions of the form $(1-x)^\\alpha(1+x)^\\beta/\\{(ax+b)^4q(x)^2\\}$, in which $q(x)$ is a polynomial in $x$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-06T14:39:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multi-indexed orthogonal polynomials",
      "apparent singularity",
      "jacobi case",
      "solvable quantum mechanical systems",
      "second order fuchsian differential equations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1751-8113/46/11/115205",
      "journal": "Journal of Physics A Mathematical General",
      "year": 2013,
      "month": "Mar",
      "volume": 46,
      "number": 11,
      "pages": 115205
    },
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1188863,
      "adsabs": "2013JPhA...46k5205H"
    }
  }
}