Global asymptotics of Stieltjes-Wigert polynomials

Yutian LI, R. Wong

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Asymptotic formulas are derived for the Stieltjes-Wigert polynomials S n(z; q) in the complex plane as the degree n grows to infinity. One formula holds in any disc centered at the origin, and the other holds outside any smaller disc centered at the origin; the two regions together cover the whole plane. In each region, the q-Airy function Aq(z) is used as the approximant. For real x > 1/4, a limiting relation is also established between the q-Airy function Aq(x) and the ordinary Airy function Ai(x) as q → 1.

Original languageEnglish
Article number1350028
JournalAnalysis and Applications
Volume11
Issue number5
DOIs
Publication statusPublished - Sep 2013

Scopus Subject Areas

  • Analysis
  • Applied Mathematics

User-Defined Keywords

  • Airy function
  • Asymptotic formulas
  • q-Airy function
  • Stieltjes-Wigert polynomials

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