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 recursion relation.
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.
| Original language | English |
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| Publisher | The Department of Electrical and Information Technology |
| Number of pages | 16 |
| Volume | TEAT-7228 |
| Publication status | Published - 2014 |
Publication series
| Name | Technical Report LUTEDX/(TEAT-7228)/1-16/(2014) |
|---|---|
| Volume | TEAT-7228 |
Bibliographical note
Published version: Journal of Mathematical Analysis and Applications, Vol. 432, No. 1, pp. 324-337, 2015.Subject classification (UKÄ)
- Electrical Engineering, Electronic Engineering, Information Engineering