期刊
ANALYSIS AND APPLICATIONS
卷 12, 期 4, 页码 463-484出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219530514500286
关键词
Asymptotic expansions; second-order linear difference equations; three-term recurrence relations; orthogonal polynomials
In this paper, we review the asymptotic results that are now available for second-order linear difference equations containing a parameter (or, equivalently, three-term recurrence relations). These include asymptotic expansions for solutions to these equations when the parameter is fixed or varying in an interval containing a turning point or a transition point. Also presented is a method for deriving asymptotic approximations for solutions when the initial values are given. These results are particularly useful when a given system of orthogonal polynomials (i) does not satisfy any second-order differential equation, (ii) does not have any integral representation, and (iii) is not even associated with a unique (or any) weight function.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据