Nonlinear equations for the recurrence coefficients of discrete orthogonal polynomials

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

9 Scopus Citations
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Author(s)

  • Mourad E.H. Ismail
  • Plamen Simeonov

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)259-274
Journal / PublicationJournal of Mathematical Analysis and Applications
Volume376
Issue number1
Publication statusPublished - 1 Apr 2011

Abstract

We study polynomials orthogonal on a uniform grid. We show that each weight function gives two potentials and each potential leads to a structure relation (lowering operator). These results are applied to derive second order difference equations satisfied by the orthogonal polynomials and nonlinear difference equations satisfied by the recursion coefficients in the three-term recurrence relations. © 2010 Elsevier Inc.

Research Area(s)

  • Discrete orthogonal polynomials, Nonlinear difference equations, Raising and lowering operators, Supplementary conditions