Parabolic cylinder functions of large order

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:190

Article; Proceedings Paper

Jones, DS

关键词: parabolic cylinder functions;    uniform asymptotic expansions;    computation of special functions;   

DOI  :  10.1016/j.cam.2005.04.009

来源: Elsevier

【 摘 要 】

The asymptotic behaviour of parabolic cylinder functions of large real order is considered. Various expansions in terms of elementary functions are derived. They hold uniformly for the variable in appropriate parts of the complex plane. Some of the expansions are doubly asymptotic with respect to the order and the complex variable which is an advantage for computational purposes. Error bounds are determined for the truncated versions of the asymptotic series. (c) 2005 Published by Elsevier B.V.

【 授权许可】

Free