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arXiv · 1302.5193

Global Asymptotics of Stieltjes-Wigert Polynomials

Y. T. Li·R. Wong
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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 $\mathrm{Ai}(x)$ as $q \to 1$.

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BibTeXRIS

Y. T. Li, R. Wong. 2013-06-11. Global Asymptotics of Stieltjes-Wigert Polynomials. https://doi.org/10.1142/s0219530513500280

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