Global Asymptotics of Stieltjes–Wigert Polynomials

Y. T. Li; R. Wong

doi:10.1142/9789814656054_0063

Global Asymptotics of Stieltjes–Wigert Polynomials

Y. T. Li, R. Wong

Research output: Chapter in book/report/conference proceeding › Chapter › peer-review

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 A_q(z) is used as the approximant. For real x > 1/4, a limiting relation is also established between the q-Airy function A_q(x) and the ordinary Airy function Ai(x) as q → 1.

Original language	English
Title of host publication	The Selected Works of Roderick S C Wong
Editors	Dan Dai, Hui Hui Dai, Tong Yang, Ding Xuan Zhou
Publisher	World Scientific Publishing Co.
Pages	1474-1485
Number of pages	12
Volume	3
ISBN (Electronic)	9789814656054, 9789814656061
ISBN (Print)	9789814656047
DOIs	https://doi.org/10.1142/9789814656054_0063
Publication status	Published - Sept 2015

Scopus Subject Areas

General Mathematics

User-Defined Keywords

Airy function
Asymptotic formulas
Q-airy function
Stieltjes-wigert polynomials

Access to Document

10.1142/9789814656054_0063

Cite this

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title = "Global Asymptotics of Stieltjes–Wigert Polynomials",

abstract = "Asymptotic formulas are derived for the Stieltjes–Wigert polynomials Sn(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.",

keywords = "Airy function, Asymptotic formulas, Q-airy function, Stieltjes-wigert polynomials",

author = "Li, {Y. T.} and R. Wong",

note = "Funding information: The work of Y. T. Li is supported by the HKBU Strategic Development Fund and a fund from HKBU (no.: 38-40-106). Publisher Copyright: {\textcopyright} 2016 by World Scientific Publishing Co. Ptc. Ltd.",

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AB - Asymptotic formulas are derived for the Stieltjes–Wigert polynomials Sn(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.

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Global Asymptotics of Stieltjes–Wigert Polynomials

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