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Please use this identifier to cite or link to this item: http://hdl.handle.net/10373/376

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Title: High-precision evaluation of the Bessel functions via Hadamard series
Authors: Paris, Richard B.
Affiliation: University of Abertay Dundee. School of Contemporary Sciences
Keywords: Hadamard series
Hyperasymptotics
Bessel functions
Confluent hypergeometric functions
Issue Date: 1-Feb-2009
Publisher: Elsevier
Type: Journal Article
Refereed: peer-reviewed
Rights: Published version (c)Elsevier, available from DOI: 10.1016/j.cam.2008.04.025
Citation: Paris, R. B. 2009. High-precision evaluation of the Bessel functions via Hadamard series. Journal of Computational and Applied Mathematics. 224(1): pp.84-100. Available from: DOI: 10.1016/j.cam.2008.04.025
Abstract: We present a method of high-precision calculation of the Bessel functions using Hadamard series. Such series are absolutely convergent expansions involving the normalised incomplete gamma function [formula missing] and possess early terms that behave like those in an asymptotic expansion. In the case of real variables the function P(a,z) acts as a smoothing factor on the terms of the series. We show how these series representing the Bessel functions of complex argument can be chosen so as to produce rapidly convergent series that possess terms decaying at the geometric rate [formula missing]k, where 0<[formula missing]<1 and k is the ordinal number of the series. We give numerical examples with [formula missing]. The theory is extended to cover the confluent hypergeometric functions [formula missing] and U(a,b,z), thereby dealing with many of the special functions arising in mathematical physics.
URI: http://hdl.handle.net/10373/376
ISSN: 0377-0427
Appears in Collections:Science Engineering & Technology Collection

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