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

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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.
Original languageEnglish
PublisherThe Department of Electrical and Information Technology
Number of pages16
VolumeTEAT-7228
Publication statusPublished - 2014

Publication series

NameTechnical Report LUTEDX/(TEAT-7228)/1-16/(2014)
VolumeTEAT-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

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