A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS

被引：2
|
作者：
Wei, Shi [1 ]
机构：
[1] Wuhan Univ, Sch Math & Stat, Wuhan 430071, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2008年 / 28卷 / 04期
关键词：
Hermite polynomials; uniform asymptotic expansion; Airy function;
D O I：
10.1016/S0252-9602(08)60084-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, the author extends the validity of a uniform asymptotic expansion of the Hermite polynomials H-n(root 2n + 1 alpha) to include all positive values of a. His method makes use of the rational functions introduced by Olde Daalhuis and Temme (SIAM J. Math. Anal., (1994), 25: 304-321). A new estimate for the remainder is given.
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页码：834 / 842
页数：9
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