Wilson多项式的渐近性

IF 2 2区 数学 Q1 MATHEMATICS
Yutian Li, Xiang-Sheng Wang, R. Wong
{"title":"Wilson多项式的渐近性","authors":"Yutian Li, Xiang-Sheng Wang, R. Wong","doi":"10.1142/S0219530519500076","DOIUrl":null,"url":null,"abstract":"In this paper, we study the asymptotic behavior of the Wilson polynomials [Formula: see text] as their degree tends to infinity. These polynomials lie on the top level of the Askey scheme of hypergeometric orthogonal polynomials. Infinite asymptotic expansions are derived for these polynomials in various cases, for instance, (i) when the variable [Formula: see text] is fixed and (ii) when the variable is rescaled as [Formula: see text] with [Formula: see text]. Case (ii) has two subcases, namely, (a) zero-free zone ([Formula: see text]) and (b) oscillatory region [Formula: see text]. Corresponding results are also obtained in these cases (iii) when [Formula: see text] lies in a neighborhood of the transition point [Formula: see text], and (iv) when [Formula: see text] is in the neighborhood of the transition point [Formula: see text]. The expansions in the last two cases hold uniformly in [Formula: see text]. Case (iv) is also the only unsettled case in a sequence of works on the asymptotic analysis of linear difference equations.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219530519500076","citationCount":"3","resultStr":"{\"title\":\"Asymptotics of the Wilson polynomials\",\"authors\":\"Yutian Li, Xiang-Sheng Wang, R. Wong\",\"doi\":\"10.1142/S0219530519500076\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study the asymptotic behavior of the Wilson polynomials [Formula: see text] as their degree tends to infinity. These polynomials lie on the top level of the Askey scheme of hypergeometric orthogonal polynomials. Infinite asymptotic expansions are derived for these polynomials in various cases, for instance, (i) when the variable [Formula: see text] is fixed and (ii) when the variable is rescaled as [Formula: see text] with [Formula: see text]. Case (ii) has two subcases, namely, (a) zero-free zone ([Formula: see text]) and (b) oscillatory region [Formula: see text]. Corresponding results are also obtained in these cases (iii) when [Formula: see text] lies in a neighborhood of the transition point [Formula: see text], and (iv) when [Formula: see text] is in the neighborhood of the transition point [Formula: see text]. The expansions in the last two cases hold uniformly in [Formula: see text]. Case (iv) is also the only unsettled case in a sequence of works on the asymptotic analysis of linear difference equations.\",\"PeriodicalId\":55519,\"journal\":{\"name\":\"Analysis and Applications\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2020-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1142/S0219530519500076\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/S0219530519500076\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/S0219530519500076","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3

摘要

在本文中,我们研究了Wilson多项式[公式:见正文]的渐近行为,因为它们的阶趋于无穷大。这些多项式位于超几何正交多项式的Askey格式的顶层。在各种情况下,这些多项式都得到了无穷的渐近展开式,例如,(i)当变量[公式:见正文]固定时,以及(ii)当变量用[公式:看正文]重新缩放为[公式:见正文]时。情况(ii)有两个子类,即(a)零自由区([公式:见正文])和(b)振荡区[公式:参见正文]。在这些情况下(iii)当[公式:参见文本]位于过渡点[公式:见文本]的邻域中时,以及(iv)当[方程式:参见文本】位于过渡点的邻域[公式:查看文本]时,也获得了相应的结果。最后两种情况下的展开式在[公式:见正文]中保持一致。案例(iv)也是关于线性差分方程渐近分析的一系列工作中唯一未解决的案例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymptotics of the Wilson polynomials
In this paper, we study the asymptotic behavior of the Wilson polynomials [Formula: see text] as their degree tends to infinity. These polynomials lie on the top level of the Askey scheme of hypergeometric orthogonal polynomials. Infinite asymptotic expansions are derived for these polynomials in various cases, for instance, (i) when the variable [Formula: see text] is fixed and (ii) when the variable is rescaled as [Formula: see text] with [Formula: see text]. Case (ii) has two subcases, namely, (a) zero-free zone ([Formula: see text]) and (b) oscillatory region [Formula: see text]. Corresponding results are also obtained in these cases (iii) when [Formula: see text] lies in a neighborhood of the transition point [Formula: see text], and (iv) when [Formula: see text] is in the neighborhood of the transition point [Formula: see text]. The expansions in the last two cases hold uniformly in [Formula: see text]. Case (iv) is also the only unsettled case in a sequence of works on the asymptotic analysis of linear difference equations.
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
CiteScore
3.90
自引率
4.50%
发文量
29
审稿时长
>12 weeks
期刊介绍: Analysis and Applications publishes high quality mathematical papers that treat those parts of analysis which have direct or potential applications to the physical and biological sciences and engineering. Some of the topics from analysis include approximation theory, asymptotic analysis, calculus of variations, integral equations, integral transforms, ordinary and partial differential equations, delay differential equations, and perturbation methods. The primary aim of the journal is to encourage the development of new techniques and results in applied analysis.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信