Global asymptotics of hermite polynomials via Riemann-Hilbert approach

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

9 Scopus Citations
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Author(s)

  • R. Wong
  • L. Zhang

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)661-682
Journal / PublicationDiscrete and Continuous Dynamical Systems - Series B
Volume7
Issue number3
Publication statusPublished - May 2007

Abstract

In this paper, we study the asymptotic behavior of the Hermite polynomials Hn((2n + 1)1/2z) as n → ∞. A globally uniform asymptotic expansion is obtained for z in an unbounded region containing the right half-plane Re z ≥ 0. A corresponding expansion can also be given for z in the left half-plane by using the symmetry property of the Hermite polynomials. Our approach is based on the steepest-descent method for Riemann-Hilbert problems introduced by Deift and Zhou.

Research Area(s)

  • Airy functions, Global asymptotics, Hermite polynomials, Riemann-Hilbert problems

Citation Format(s)