Certain integral transforms involving Appell and Bessel functions and their applications

Abstract This paper deals with the evaluation of certain integral transforms involving the product of certain Appell and Bessel functions with a weight e - γ ⁢ t 2 {e^{-\gamma t^{2}}} . The transformations of these integrals are evaluated in terms of the Appell, Kampé de Fériet and the triple hypergeometric functions. As an application, we studied propagation of generalized Humbert–Gaussian beams (GHGBs) and hypergeometric-Gaussian beams (HyGGBs) in turbulent atmosphere and through an ABCD paraxial optical system. The evaluation of these integral transforms has initiated a great interest in mathematical physics and its applications to laser physics and linear or non-linear optics.