The asymptotic expansions of Hankel transforms and related integrals
Author:
Robert F. MacKinnon
Journal:
Math. Comp. 26 (1972), 515-527
MSC:
Primary 44A15
DOI:
https://doi.org/10.1090/S0025-5718-1972-0308695-9
MathSciNet review:
0308695
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Abstract: In this paper, the asymptotic expansion of integrals of the form s considered, as
tends to infinity, and where
are Bessel functions of the first and second kind, or functions closely related to these. Asymptotic expansions for several functions of this type are presented under suitable restrictions on
. The expansion given by Willis for Hankel transforms is seen to be valid under conditions of
less restrictive than those imposed by that author.
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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1972-0308695-9
Keywords:
Asymptotic expansion,
far-field approximation,
integral transforms,
Hankel transforms,
Bessel functions,
cylindrical functions,
sine integral,
Fresnel integral
Article copyright:
© Copyright 1972
American Mathematical Society