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Zbl 1087.33010
Jones, D.S.
Parabolic cylinder functions of large order. (English)
[J] J. Comput. Appl. Math. 190, No. 1-2, 453-469 (2006). ISSN 0377-0427

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.
[Francisco Perez Acosta (La Laguna)]

MSC 2000:: *33E30 Functions coming from diff., difference and integral equations

Keywords: parabolic cylinder functions; uniform asymptotic expansions; computation of special functions

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