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Parabolic cylinder functions of large order. (English) Zbl 1087.33010
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.
MSC:
33E30Functions coming from differential, difference and integral equations