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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) TEAT-7228.
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)
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author
organization
publishing date
type
Book/Report
publication status
published
subject
in
Technical Report LUTEDX/(TEAT-7228)/1-16/(2014)
volume
TEAT-7228
pages
16 pages
publisher
[Publisher information missing]
language
English
LU publication?
yes
id
35d2f720-013a-4c2e-9ba0-cdca45904744 (old id 4253213)
date added to LUP
2014-01-27 13:27:21
date last changed
2016-08-30 13:32:35
@misc{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},
  language     = {eng},
  pages        = {16},
  publisher    = {ARRAY(0xa70cab0)},
  series       = {Technical Report LUTEDX/(TEAT-7228)/1-16/(2014)},
  title        = {Evaluation of some integrals relevant to multiple scattering by randomly distributed obstacles},
  volume       = {TEAT-7228},
  year         = {2014},
}