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

Kristensson, Gerhard LU (2015) In Journal of Mathematical Analysis and Applications 432(1). p.324-337
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 closed formula.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Mathematical Analysis and Applications
volume
432
issue
1
pages
324 - 337
publisher
Elsevier
external identifiers
  • wos:000359030800021
  • scopus:84937817571
ISSN
0022-247X
DOI
10.1016/j.jmaa.2015.06.047
language
English
LU publication?
yes
id
86050945-9aeb-4d5a-9ded-afe31efd2cc6 (old id 7471156)
date added to LUP
2015-07-20 10:13:47
date last changed
2017-01-01 05:48:54
@article{86050945-9aeb-4d5a-9ded-afe31efd2cc6,
  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 closed formula.},
  author       = {Kristensson, Gerhard},
  issn         = {0022-247X},
  language     = {eng},
  number       = {1},
  pages        = {324--337},
  publisher    = {Elsevier},
  series       = {Journal of Mathematical Analysis and Applications},
  title        = {Evaluation of some integrals relevant to multiple scattering by randomly distributed obstacles},
  url          = {http://dx.doi.org/10.1016/j.jmaa.2015.06.047},
  volume       = {432},
  year         = {2015},
}