Evaluation of some integrals relevant to multiple scattering by randomly distributed obstacles
(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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/4253213
- author
- Kristensson, Gerhard ^{LU}
- organization
- publishing date
- 2014
- type
- Book/Report
- publication status
- published
- subject
- in
- Technical Report LUTEDX/(TEAT-7228)/1-16/(2014)
- volume
- TEAT-7228
- pages
- 16 pages
- publisher
- The Department of Electrical and Information Technology
- 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
- 2017-10-13 10:33:34
@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}, pages = {16}, 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}, }