In this paper, we employ a difference equation approach to study the Plancherel‐Rotach asymptotics of ‐orthogonal polynomials about their largest zeros. Our method for ‐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 and ‐Hermite polynomials.

中文翻译：

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正交多项式Plancherel-Rotach渐近的差分方程方法

在本文中，我们采用差分方程方法研究正交多项式在其最大零点附近的Plancherel- Rotach渐近性。我们的差分方程方法类似于Hermite微分方程的转折点问题。它在Stieltjes-Wigert多项式和-Hermite多项式的玩具问题中效果很好。