• Title of article

    Some Orthogonal Polynomials Related to Elliptic Functions Original Research Article

  • Author/Authors

    Mourad E.H. Ismail ، نويسنده , , Christina T?nnesen-Friedman and Galliano Valent، نويسنده , , Gang J. Yoon، نويسنده ,

  • Issue Information
    روزنامه با شماره پیاپی سال 2001
  • Pages
    28
  • From page
    251
  • To page
    278
  • Abstract
    We characterize the orthogonal polynomials in a class of polynomials defined through their generating functions. This led to three new systems of orthogonal polynomials whose generating functions and orthogonality relations involve elliptic functions. The Hamburger moment problems associated with these polynomials are indeterminate. We give infinite families of weight functions in each case. The different polynomials treated in this work are also polynomials in a parameter and as functions of this parameter they are orthogonal with respect to unique measures, which we find explicitly. Through a quadratic transformation we find a new exactly solvable birth and death process with quartic birth and death rates.
  • Journal title
    Journal of Approximation Theory
  • Serial Year
    2001
  • Journal title
    Journal of Approximation Theory
  • Record number

    851958