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GLOBAL ASYMPTOTICS OF STIELTJES–WIGERT POLYNOMIALS

Institute of Computational and Theoretical Studies and Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong

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and

R. WONG

Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, Kowloon, Hong Kong

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https://doi.org/10.1142/S0219530513500280Cited by:5 (Source: Crossref)

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.

Keywords:

AMSC: 41A60, 33C45

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