Asymptotic Expansions of Integrals. Norman Bleistein , Richard A. Asymptotic analysis, that branch of mathematics devoted to the study of the behavior of functions within chosen limits, was once thought of more as a specialized art than a necessary discipline. Now, a solid foundation in the theory and technique of asymptotic expansion of integrals is at the heart of the education of every student concentrating in applied mathematics. It is also an invaluable asset to scientists in many other fields.
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We'd like to understand how you use our websites in order to improve them. Register your interest. In this limit the results of the classical methods of stationary phase and steepest descents become invalid. The motivating physical problem is the propagation of signals in dispersive media. The technique used to obtain the uniform expansion is an adaptation of the method originally developed by Chester , Friedman and Ursell in their treatment of the problem of two nearby stationary points.
Here, however, we find that a certain family of Bessel functions play the role of the Airy functions in that problem. In fact a theorem is proved which establishes the asymptotic nature of our results in the relevant limits.
Finally, two examples are considered to illustrate the use of these results. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Bleistein , N. Pure Appl. Google Scholar. Handelsman , Uniform asymptotic expansion of certain integrals. SIAM J. Chester , C. Ursell , An extension of the method of steepest descents. Friedman , B.
SIAM Journal 7 , — Lewis , R. Sommerfeld , A. Lectures in Theoretical Physics, IV, paperback edition. New York: Academic Press Ursell , F.
Whitham , G. Pure and Appl. Whittaker , E. Cambridge University Press Download references. Reprints and Permissions. Handelsman, R. Uniform asymptotic expansions of integrals that arise in the analysis of precursors. Rational Mech. Download citation. Received : 03 June Issue Date : January Search SpringerLink Search. Immediate online access to all issues from Subscription will auto renew annually. References Bleistein , N. Handelsman View author publications.
You can also search for this author in PubMed Google Scholar. View author publications. Additional information Communicated by C. Rights and permissions Reprints and Permissions. About this article Cite this article Handelsman, R.
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Asymptotic Expansion of Integrals
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Uniform asymptotic expansions of integrals that arise in the analysis of precursors
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