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Title: Exactification of the method of steepest descents: the Bessel functions of large order and argument
Authors: Paris, Richard B.
Affiliation: University of Abertay Dundee. School of Contemporary Sciences
Keywords: Asymptotics
Hyperasymptotics
Hadamard expansions
Laplace-type integrals
Method of steepest descents
Bessel functions
Issue Date: Sep-2004
Publisher: The Royal Society
Type: Journal Article
Refereed: peer-reviewed
Rights: Published version (c)The Royal Society, available from DOI: 10.1098/rspa.2004.1307
Citation: Paris, R. B. 2004. Exactification of the method of steepest descents: the Bessel functions of large order and argument. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 460(2049): pp.2737-2759. [Online] Available from: DOI: 10.1098/rspa.2004.1307
Abstract: The Hadamard expansion procedure applied to Laplace–type integrals taken along contours in the complex plane enables an exact description of the method of steepest descents. This mode of expansion is illustrated by the evaluation of the Bessel functions Jv(? x) and Yv(v x) of large order and argument when x is bounded away from unity. The limit x → 1, corresponding to the coalescence of the active saddles in the integral representations of the Bessel functions, translates into a progressive loss of exponential separation between the different levels of the Hadamard expansion, which renders computation in this limit more difficult. It is shown how a simple modification to this procedure can be employed to deal with the coalescence of the active saddles when x → 1.
URI: http://hdl.handle.net/10373/302
ISSN: 1471-2946
Appears in Collections:Science Engineering & Technology Collection

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