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Please use this identifier to cite or link to this item: http://hdl.handle.net/10373/267

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Title: On the use of Hadamard expansions in hyperasymptotic evaluation: differential equations of hypergeometric type
Authors: Kaminski, D.
Paris, Richard B.
Affiliation: University of Abertay Dundee. School of Computing and Creative Technologies
Keywords: Hadamard expansions
Differential equations
Issue Date: 2004
Publisher: Cambridge University Press
Type: Journal Article
Refereed: peer-reviewed
Rights: Published version (c)2004 Royal society of Edinburgh available online from Cambridge University Press at doi:10.1017/S0308210500003139
Citation: Kaminski, D. and Paris, R.B. 2004. On the use of Hadamard expansions in hyperasymptotic evaluation: differential equations of hypergeometric type. Proceedings of the Royal Societ of Edinburgh. 134A. pp.159-178
Abstract: We describe how a modification of a common technique for developing asymptotic expansions of solutions of linear differential equations can be used to derive Hadamard expansions of solutions of differential equations. Hadamard expansions are convergent series that share some of the features of hyperasymptotic expansions, particularly that of having exponentially small remainders when truncated, and, as a consequence, provide a useful computational tool for evaluating special functions. The methods we discuss can be applied to linear differential equations of hypergeometric type and may have wider applicability.
URI: http://hdl.handle.net/10373/267
ISSN: 1473-7124
Appears in Collections:Computing & Engineering Systems Collection

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