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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 $ \int_0^\infty {F(kr)f(k)dk} $ s considered, as $ r$ tends to infinity, and where $ F(kr)$ 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 $ f(k)$. The expansion given by Willis for Hankel transforms is seen to be valid under conditions of $ f(k)$ less restrictive than those imposed by that author.


References [Enhancements On Off] (What's this?)

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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

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