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On the resurgence properties of the uniform asymptotic expansion of Bessel functions of high order

On the resurgence properties of the uniform asymptotic expansion of Bessel functions of high order
On the resurgence properties of the uniform asymptotic expansion of Bessel functions of high order
For the coefficients An(‘) and Bn(‘), that occur in the uniform asymptotic expansions of Bessel functions of large order, we give asymptotic expansions as n M X. The coefficients in these asymptotic expansions are again Am>(‘) and Bm(‘), and the asymptotic base consists of functions Apq(n,‘), which can be seen as new generalizations of the Airy function. We describe the asymptotic behaviour of the functions Apq(n, ‘), as n to infinity, and we compute the Taylor-series expansions of Apq(n, ‘) at ‘ = 0. Two numerical examples are included.
1364-5021
3917-3930
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Daalhuis, A.B. Olde
d2254863-03c9-4e12-aee7-2855b60dc933
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Daalhuis, A.B. Olde
d2254863-03c9-4e12-aee7-2855b60dc933

Howls, C.J. and Daalhuis, A.B. Olde (1999) On the resurgence properties of the uniform asymptotic expansion of Bessel functions of high order. Proceedings of the Royal Society A, 455 (1991), 3917-3930. (doi:10.1098/rspa.1999.0483).

Record type: Article

Abstract

For the coefficients An(‘) and Bn(‘), that occur in the uniform asymptotic expansions of Bessel functions of large order, we give asymptotic expansions as n M X. The coefficients in these asymptotic expansions are again Am>(‘) and Bm(‘), and the asymptotic base consists of functions Apq(n,‘), which can be seen as new generalizations of the Airy function. We describe the asymptotic behaviour of the functions Apq(n, ‘), as n to infinity, and we compute the Taylor-series expansions of Apq(n, ‘) at ‘ = 0. Two numerical examples are included.

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Published date: 1999

Identifiers

Local EPrints ID: 29204
URI: http://eprints.soton.ac.uk/id/eprint/29204
ISSN: 1364-5021
PURE UUID: 434ac63a-47eb-4c7d-ae3d-bc003b6c88c1
ORCID for C.J. Howls: ORCID iD orcid.org/0000-0001-7989-7807

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Date deposited: 21 Jul 2006
Last modified: 07 Oct 2020 01:44

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