On a class of definite integrals with products of (Ricatti-)Bessel functions and their derivatives

Abstract

In certain physical processes such as in light scattering and absorption by lossy concentric spherical particles, there exist integrals of products between (Ricatti-)Bessel functions and derivatives of (Ricatti-)Bessel functions of arbitrary kind, integer order and complex argument. This paper presents an analytical solution to such integrals which, to the best of the authors’ knowledge, has not been reported elsewhere in the literature. As a consequence, we also establish analytical expressions for similar integrals in terms of Bessel functions and their derivatives.