{
  "id": "math/9404224",
  "version": "v1",
  "published": "1994-04-22T00:00:00.000Z",
  "updated": "1994-04-22T00:00:00.000Z",
  "title": "Explicit representations of biorthogonal polynomials",
  "authors": [
    "Arieh Iserles",
    "Syvert Paul Nørsett"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Given a parametrised weight function $\\omega(x,\\mu)$ such that the quotients of its consecutive moments are M\\\"obius maps, it is possible to express the underlying biorthogonal polynomials in a closed form \\cite{IN2}. In the present paper we address ourselves to two related issues. Firstly, we demonstrate that, subject to additional assumptions, every such $\\omega$ obeys (in $x$) a linear differential equation whose solution is a generalized hypergeometric function. Secondly, using a generalization of standard divided differences, we present a new explicit representation of the underlying orthogonal polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1994-04-22T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "explicit representation",
      "linear differential equation",
      "underlying orthogonal polynomials",
      "standard divided differences",
      "generalized hypergeometric function"
    ],
    "publication": {
      "doi": "10.1007/BF02198296",
      "journal": "Numerical Algorithms",
      "year": 1995,
      "month": "Mar",
      "volume": 10,
      "number": 1,
      "pages": 51
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1995NuAlg..10...51I"
    }
  }
}