Analytical results for a Bessel function times Legendre polynomials class integrals

TL;DR

This paper derives an analytical expression for integrals involving Bessel functions and Legendre polynomials, simplifying calculations in electromagnetic vector diffraction problems and eliminating the need for numerical methods.

Contribution

It provides a new analytical solution for a class of integrals involving Bessel and Legendre functions relevant to electromagnetic theory.

Findings

Analytical formula for Bessel-Legendre integrals derived.

Simplifies calculations in electromagnetic vector diffraction.

Reduces reliance on numerical quadrature techniques.

Abstract

When treating problems of vector diffraction in electromagnetic theory, the evaluation of the integral involving Bessel and associated Legendre functions is necessary. Here we present the analytical result for this integral that will make unnecessary numerical quadrature techniques or localized approximations. The solution is presented using the properties of the Bessel and associated Legendre functions.