An Integral Transform Involving the Product Of Bessel Functions and Whittaker Function and Its Application

Abstract

In this paper, we aim to establish a closed form for an integral transform involving the product of two Bessel functions of the first kind and the Whittaker function. This integral transform is evaluated in terms of the Lauricella’s triple hypergeometric function, which reduces to the generalized Kampe de Feriet function and is interesting to generate some new laser beams and to study the propagation of these waves through free space and atmospheric and maritime turbulent. Besides, some particular cases are derived by using the relations between the Whittaker function and other special functions and orthogonal polynomials. A novel beams family, called “ Lauricella beams ” is introduced and the propagation of Laguerre–Bessel–Gaussian beam through an ABCD optical system is studied.