On analytical solutions to classes of definite integrals with products of Bessel functions of the first kind and their derivatives

In certain physical problems of light scattering, classes of integrals appear which involve particular products of Bessel functions of the first kind with complex argument and integer orders n and n +/- 1 (-infinity <= n <= infinity), and also products of derivatives of such Bessel functions. Due to the lack of available analytical solutions in the literature, numerical calculations of these integrals have been recently carried out for the evaluation of photophoretic asymmetry factors (PAFs) in problems involving the illumination of lossy infinite cylinders, either in isolation or close to conducting corner spaces or planar boundaries, by plane waves or light-sheets. Here, we show that these integrals can actually be resolved analytically, therefore allowing for faster computation of physical quantities of interest in light scattering by small particles. (C) 2022 Published by Elsevier Ltd.

Automated summary

This study investigates a class of integrals in light scattering, and demonstrates that resolving these integrals analytically allows for faster evaluation of photophoretic asymmetry factors. This is crucial for studying light scattering by small particles.