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

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Author

Summary, in English

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.

Publishing year

2015

Language

English

Pages

324-337

Publication/Series

Journal of Mathematical Analysis and Applications

Volume

432

Issue

1

Document type

Journal article

Publisher

Elsevier

Topic

  • Electrical Engineering, Electronic Engineering, Information Engineering

Status

Published

Research group

  • Electromagnetic theory

ISBN/ISSN/Other

  • ISSN: 0022-247X