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Evaluation of some integrals relevant to multiple scattering by randomly distributed obstacles

Kristensson, Gerhard LU (2014) In Technical Report LUTEDX/(TEAT-7228)/1-16/(2014)
Abstract
This paper analyzes and solves an integral and its indefinite Fourier transform of importance in multiple scattering problems of randomly distributed scatterers.

The integrand contains a radiating spherical wave, and the two-dimensional domain of integration excludes a circular region of varying size.

A solution of the integral in terms of radiating spherical waves is demonstrated. The method employs the Erdelyi operators, which leads to a recursion relation. This recursion relation is solved in terms of a finite sum of radiating spherical waves.

The solution of the indefinite Fourier transform of the integral contains the indefinite Fourier transforms of the Legendre polynomials, which are solved by a... (More)
This paper analyzes and solves an integral and its indefinite Fourier transform of importance in multiple scattering problems of randomly distributed scatterers.

The integrand contains a radiating spherical wave, and the two-dimensional domain of integration excludes a circular region of varying size.

A solution of the integral in terms of radiating spherical waves is demonstrated. The method employs the Erdelyi operators, which leads to a recursion relation. This recursion relation is solved in terms of a finite sum of radiating spherical waves.

The solution of the indefinite Fourier transform of the integral contains the indefinite Fourier transforms of the Legendre polynomials, which are solved by a recursion relation. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Book/Report
publication status
published
subject
in
Technical Report LUTEDX/(TEAT-7228)/1-16/(2014)
pages
16 pages
publisher
The Department of Electrical and Information Technology
report number
TEAT-7228
language
English
LU publication?
yes
additional info
Published version: Journal of Mathematical Analysis and Applications, Vol. 432, No. 1, pp. 324-337, 2015.
id
35d2f720-013a-4c2e-9ba0-cdca45904744 (old id 4253213)
date added to LUP
2016-04-04 14:21:50
date last changed
2018-11-21 21:19:52
@techreport{35d2f720-013a-4c2e-9ba0-cdca45904744,
  abstract     = {{This paper analyzes and solves an integral and its indefinite Fourier transform of importance in multiple scattering problems of randomly distributed scatterers.<br/><br>
 The integrand contains a radiating spherical wave, and the two-dimensional domain of integration excludes a circular region of varying size.<br/><br>
 A solution of the integral in terms of radiating spherical waves is demonstrated. The method employs the Erdelyi operators, which leads to a recursion relation. This recursion relation is solved in terms of a finite sum of radiating spherical waves.<br/><br>
 The solution of the indefinite Fourier transform of the integral contains the indefinite Fourier transforms of the Legendre polynomials, which are solved by a recursion relation.}},
  author       = {{Kristensson, Gerhard}},
  institution  = {{The Department of Electrical and Information Technology}},
  language     = {{eng}},
  number       = {{TEAT-7228}},
  series       = {{Technical Report LUTEDX/(TEAT-7228)/1-16/(2014)}},
  title        = {{Evaluation of some integrals relevant to multiple scattering by randomly distributed obstacles}},
  url          = {{https://lup.lub.lu.se/search/files/6343087/4253214.pdf}},
  year         = {{2014}},
}