二次系数差分方程的渐近分析

IF 0.6 Q4 MATHEMATICS, APPLIED
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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
Methods and applications of analysis MATHEMATICS, APPLIED-
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