Parabolic cylinder functions of large order

Authors:
D. S. Jones
Affiliations:
Department of Mathematics, University of Dundee, Scotland, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 2
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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.