A difference equation approach to Plancherel-Rotach asymptotics forq-orthogonal polynomials

被引：0
|
作者：
Ismail, Mourad [1 ]
Law, Chun-Kong [2 ]
机构：
[1] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA
[2] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan
来源：
STUDIES IN APPLIED MATHEMATICS | 2020年 / 145卷 / 04期
关键词：
<mml; math altimg="urn; x-wiley; 00222526; media; sapm12332; sapm12332-math-0002" display="inline"><mml; mi>q</mml; mi></mml; math>-Airy function; sapm12332-math-0003" display="inline"><mml; math>-difference equations; sapm12332-math-0004" display="inline"><mml; msup><mml; mi><mml; mrow><mml; mo>-</mml; mo><mml; mn>1</mml; mn></mml; mrow></mml; msup></mml; math>-Hermite polynomials; Stieltjes-Wigert polynomials; turning point problem; BESSEL; ZEROS;
D O I：
10.1111/sapm.12332
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we employ a difference equation approach to study the Plancherel-Rotach asymptotics ofq-orthogonal polynomials about their largest zeros. Our method forq-difference equations is an analogue to the turning point problem for Hermite differential equations. It works well in the toy problems of Stieltjes-Wigert polynomials andq-1-Hermite polynomials.
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页码：696 / 718
页数：23
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