Parabolic Cylinder Functions: Examples of Error Bounds For Asymptotic Expansions

Details Parabolic Cylinder Functions: Examples of Error Bounds For Asymptotic Expansions Parabolic Cylinder Functions: Examples of Error Bounds For Asymptotic Expansions

2002-05-06

arxiv.org/abs/math/0205045v1

Mathematics

Classical Analysis and ODEs

22 pages, 4 figures

Scientific paper

Several asymptotic expansions of parabolic cylinder functions are discussed and error bounds for remainders in the expansions are presented. In particular Poincar{\'e}-type expansions for large values of the argument $z$ and uniform expansions for large values of the parameter are considered. The expansions are based on those given in Olver(1959) and on modifications of these expansions given in Temme(2000). Computer algebra techniques are used for obtaining representations of the bounds and for numerical computations.

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