A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS

doi:10.1016/S0252-9602(08)60084-3

数学物理学报(英文版)

A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS

史薇

武汉大学数学与统计学院, 武汉 430072

收稿日期:2006-08-14 修回日期:1900-01-01 出版日期:2008-10-20 发布日期:2008-10-20
通讯作者: 史薇

A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS

Shi Wei

School of Mathematics and Statistics, Wuhan University, Wuhan 430071, China

Received:2006-08-14 Revised:1900-01-01 Online:2008-10-20 Published:2008-10-20
Contact: Shi Wei

摘要/Abstract

摘要：

In this article, the author extends the validity of a uniform asymptotic expansion of the Hermite polynomials H_n(2n+1α) to include all positive values of α. 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.

关键词: Hermite polynomials, uniform asymptotic expansion, Airy function

Abstract:

Key words: Hermite polynomials, uniform asymptotic expansion, Airy function

中图分类号:

41A60

史薇. A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS[J]. 数学物理学报(英文版), 2008, 28(4): 834-842.

Shi Wei. A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS[J]. Acta mathematica scientia,Series B, 2008, 28(4): 834-842.

A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS

A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS

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