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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Vydáno v:Journal of computational and applied mathematics Ročník 190; číslo 1; s. 453 - 469
Hlavní autor: Jones, D.S.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.06.2006
Témata:
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
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Shrnutí: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.
Bibliografie:SourceType-Scholarly Journals-2
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ObjectType-Conference Paper-1
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SourceType-Conference Papers & Proceedings-1
ObjectType-Article-3
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2005.04.009