Parabolic cylinder functions of large order

D. S. Jones

doi:10.1016/j.cam.2005.04.009

Parabolic cylinder functions of large order

D. S. Jones

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	453-469
Number of pages	17
Journal	Journal of Computational and Applied Mathematics
Volume	190
Issue number	1-2
DOIs	https://doi.org/10.1016/j.cam.2005.04.009
Publication status	Published - 2006

Keywords

Parabolic cylinder functions
Uniform asymptotic expansions
Computation of special functions

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10.1016/j.cam.2005.04.009

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title = "Parabolic cylinder functions of large order",

abstract = "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.",

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AB - 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.

KW - Parabolic cylinder functions

KW - Uniform asymptotic expansions

KW - Computation of special functions

U2 - 10.1016/j.cam.2005.04.009

DO - 10.1016/j.cam.2005.04.009

M3 - Article

SN - 0377-0427

VL - 190

SP - 453

EP - 469

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1-2

ER -

Parabolic cylinder functions of large order

Abstract

Keywords

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