{
  "id": "math-ph/0501057",
  "version": "v1",
  "published": "2005-01-22T02:49:30.000Z",
  "updated": "2005-01-22T02:49:30.000Z",
  "title": "Orthogonal polynomials with discontinuous weights",
  "authors": [
    "Yang Chen",
    "Gunnar Pruessner"
  ],
  "comment": "9 pages, 2 figures, JPA style",
  "journal": "J. Phys. A: Math. Gen. 38 (12), L191--L198 (2005)",
  "doi": "10.1088/0305-4470/38/12/L01",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "In this paper we present a brief description of a ladder operator formalism applied to orthogonal polynomials with discontinuous weights. The two coefficient functions, A_n(z) and B_n(z), appearing in the ladder operators satisfy the two fundamental compatibility conditions previously derived for smooth weights. If the weight is a product of an absolutely continuous reference weight w_0 and a standard jump function, then A_n(z) and B_n(z) have apparent simple poles at these jumps. We exemplify the approach by taking w_0 to be the Hermite weight. For this simpler case we derive, without using the compatibility conditions, a pair of difference equations satisfied by the diagonal and off-diagonal recurrence coefficients for a fixed location of the jump. We also derive a pair of Toda evolution equations for the recurrence coefficients which, when combined with the difference equations, yields a particular Painleve IV.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-22T02:49:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "orthogonal polynomials",
      "discontinuous weights",
      "difference equations",
      "standard jump function",
      "fundamental compatibility conditions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}