二次系数差分方程的渐近分析

IF 0.6 Q4 MATHEMATICS, APPLIED

Methods and applications of analysis Pub Date : 2016-01-01 DOI:10.4310/MAA.2016.V23.N2.A2

Xiang-Sheng Wang

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引用次数: 0

摘要

本文研究二阶二次系数差分方程的渐近解。根据参数值，我们将差分方程分为三种情况，并分别导出了解的Plancherel-Rotach型渐近公式。作为我们主要结果的直接应用，我们还分别给出了相关的Meixner- pollaczek多项式、相关的Meixner多项式和相关的Laguerre多项式的渐近公式。

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Asymptotic analysis of difference equations with quadratic coefficients

In this paper, we study asymptotic solutions of second-order difference equations with quadratic coefficients. According to the parameter values, we classify the difference equations into three cases and derive Plancherel-Rotach type asymptotic formulas of the solutions respectively. As direct applications of our main results, we also provide asymptotic formulas of associated Meixner-Pollaczek polynomials, associated Meixner polynomials, and associated Laguerre polynomials, respectively.

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来源期刊

Methods and applications of analysis MATHEMATICS, APPLIED-

自引率

33.30%

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