Uniform asymptotics of some q-orthogonal polynomials

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

4 Scopus Citations
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Author(s)

  • X. S. Wang
  • R. Wong

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)79-87
Journal / PublicationJournal of Mathematical Analysis and Applications
Volume364
Issue number1
Publication statusPublished - 1 Apr 2010

Abstract

Uniform asymptotic formulas are obtained for the Stieltjes-Wigert polynomial, the q-1-Hermite polynomial and the q-Laguerre polynomial as the degree of the polynomial tends to infinity. In these formulas, the q-Airy polynomial, defined by truncating the q-Airy function, plays a significant role. While the standard Airy function, used frequently in the uniform asymptotic formulas for classical orthogonal polynomials, behaves like the exponential function on one side and the trigonometric functions on the other side of an extreme zero, the q-Airy polynomial behaves like the q-Airy function on one side and the q-Theta function on the other side. The last two special functions are involved in the local asymptotic formulas of the q-orthogonal polynomials. It seems therefore reasonable to expect that the q-Airy polynomial will play an important role in the asymptotic theory of the q-orthogonal polynomials. © 2009 Elsevier Inc. All rights reserved.

Research Area(s)

  • q-Airy function, q-Laguerre polynomial, q-Theta function, q-1-Hermite polynomial, Stieltjes-Wigert polynomial