Evaluation of some integrals relevant to multiple scattering by randomly distributed obstacles
(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:
https://lup.lub.lu.se/record/7471156
- author
- Kristensson, Gerhard LU
- organization
- publishing date
- 2015
- 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
- 2016-04-01 13:40:58
- date last changed
- 2022-01-27 20:26:22
@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}}, doi = {{10.1016/j.jmaa.2015.06.047}}, volume = {{432}}, year = {{2015}}, }