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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:432

Article

Kristensson, Gerhard

关键词: Erdelyi operator;    Spherical waves;    Scattering by random objects;    Pair correlation function;   

DOI  :  10.1016/j.jmaa.2015.06.047

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free