Plancherel-Rotach Asymptotic Expansion for Some Polynomials from Indeterminate Moment Problems

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

11 Scopus Citations
View graph of relations

Author(s)

  • Dan Dai
  • Mourad E.H. Ismail
  • Xiang-Sheng Wang

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)61-104
Journal / PublicationConstructive Approximation
Volume40
Issue number1
Online published1 Oct 2013
Publication statusPublished - Aug 2014

Abstract

We study the Plancherel-Rotach asymptotics of four families of orthogonal polynomials: the Chen-Ismail polynomials, the Berg-Letessier-Valent polynomials, and the Conrad-Flajolet polynomials I and II. All these polynomials arise in indeterminate moment problems, and three of them are birth and death process polynomials with cubic or quartic rates. We employ a difference equation asymptotic technique due to Z. Wang and R. Wong. Our analysis leads to a conjecture about large degree behavior of polynomials orthogonal with respect to solutions of indeterminate moment problems. © 2013 Springer Science+Business Media New York.

Research Area(s)

  • Asymptotics, Asymptotics of zeros, Difference equation technique, Indeterminate moment problems, Nevanlinna functions, Plancherel-Rotach asymptotics, The Berg-Letessier-Valent polynomials, The Chen-Ismail polynomials, The Conrad-Flajolet polynomials, Turning points