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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.
Please use this url to cite or link to this publication:
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
Academic Press
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
2016-04-01 13:40:58
date last changed
2025-11-19 10:34:57
@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    = {{Academic Press}},
  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}},
  doi          = {{10.1016/j.jmaa.2015.06.047}},
  volume       = {{432}},
  year         = {{2015}},
}