Asymptotics of orthogonal polynomials with asymptotic Freud-like weights

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

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Author(s)

  • Wen-Gao Long
  • Dan Dai
  • Yu-Tian Li
  • Xiang-Sheng Wang

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)133-163
Journal / PublicationStudies in Applied Mathematics
Volume144
Issue number2
Online published6 Dec 2019
Publication statusPublished - Feb 2020

Abstract

We derive uniform asymptotic expansions for polynomials orthogonal with respect to a class of weight functions that are real analytic and behave asymptotically like the Freud weight at infinity. Although the limiting zero distributions are the same as in the Freud cases, the asymptotic expansions are different due to the fact that the weight functions may have a finite or infinite number of zeros on the imaginary axis. To resolve the singularities caused by these zeros, an auxiliary function is introduced in the Riemann–Hilbert analysis. Asymptotic formulas are established in several regions covering the whole complex plane. We take the continuous dual Hahn polynomials as an example to illustrate our main results. Some numerical verifications are also given.

Research Area(s)

  • asymptotic approximation, asymptotic Freud-like weight, continuous dual Hahn polynomials, Riemann–Hilbert problem

Citation Format(s)

Asymptotics of orthogonal polynomials with asymptotic Freud-like weights. / Long, Wen-Gao; Dai, Dan; Li, Yu-Tian; Wang, Xiang-Sheng.

In: Studies in Applied Mathematics, Vol. 144, No. 2, 02.2020, p. 133-163.

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