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

{"title":"二次系数差分方程的渐近分析","authors":"Xiang-Sheng Wang","doi":"10.4310/MAA.2016.V23.N2.A2","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymptotic analysis of difference equations with quadratic coefficients\",\"authors\":\"Xiang-Sheng Wang\",\"doi\":\"10.4310/MAA.2016.V23.N2.A2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":18467,\"journal\":{\"name\":\"Methods and applications of analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2016-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Methods and applications of analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4310/MAA.2016.V23.N2.A2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Methods and applications of analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/MAA.2016.V23.N2.A2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

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。

查看原文本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Methods and applications of analysis MATHEMATICS, APPLIED-

自引率

33.30%

发文量