Computation of integral transforms in terms of double hypergeometric series ψ2 with applications

Abstract

The principal aim of the present paper is to evaluate a new integral transform involving the product of two Bessel Functions of the first kind expressed in terms of the Humbert function ψ₂. We also derive some interesting special cases from the main result of this paper. The presented result will be applied to generate some new laser beams called as the Humbert beams of type-II and study there propagation behaviour. From graphical simulations this type of wave seems interesting and useful in optical trapping which is used in some applications for pushing and moving particles such as: biological cells, neutral atoms, fluorescent, DNA molecules and trapping productivity on nano-sized spheres.