## 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) |
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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