Parabolic cylinder functions of large order

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 th...

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Bibliographic Details
Published in:	Journal of computational and applied mathematics Vol. 190; no. 1; pp. 453 - 469
Main Author:	Jones, D.S.
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.06.2006
Subjects:	Computation of special functions Parabolic cylinder functions Uniform asymptotic expansions Parabolic cylinder functions Computation of special functions Uniform asymptotic expansions
ISSN:	0377-0427, 1879-1778
Online Access:	Get full text
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Summary:	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.
Bibliography:	SourceType-Scholarly Journals-2 ObjectType-Feature-2 ObjectType-Conference Paper-1 content type line 23 SourceType-Conference Papers & Proceedings-1 ObjectType-Article-3
ISSN:	0377-0427 1879-1778
DOI:	10.1016/j.cam.2005.04.009