Parabolic Cylinder Functions: Examples of Error Bounds For Asymptotic Expansions

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Several asymptotic expansions of parabolic cylinder functions are discussed and error bounds for remainders in the expansions are presented. In particular Poincar{é}-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.
22 pages, 4 figures

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Classical Analysis and ODEs, 41A60 (Primary) 33C15, 33C10, 30E15, 33F05, 65D20 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/63982

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0205045
 http://arxiv.org/abs/math/0205045

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arXiv