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2.—Asymptotic Behaviour of an Aperture Integral

Published online by Cambridge University Press:  14 February 2012

D. S. Jones
D. S. Jones
Affiliation:
Department of Mathematics, University of Dundee
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Synopsis

The asymptotic behaviour of double integrals over a portion of the plane is investigated when the integrand contains an exponential factor with a large parameter. The exponent can have a stationary point which may or may not be close to the boundary of the domain of integration. Results are first derived for a rectangular region with a particularly simple exponent in the integrand and shown to be uniformly valid under certain conditions. In some circumstances the asymptotic terms can be evaluated by means of a universal function. The theory is then generalised to cover more complicated exponents and arbitrary wedge-shaped domains; it is found that the asymptotic behaviour can still be expressed in terms of the same universal function.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 71 , Issue 1 , 1972 , pp. 9 - 29
Copyright
Copyright © Royal Society of Edinburgh 1972

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