Integral transforms involving the product of Humbert and Bessel functions and its application

Abstract

In this paper, we develop some integral transforms involving a product of Humbert and Bessel functions with a weight e-γx2. These integral transforms will be evaluated in terms of hypergeometric functions. Various transformation formulae are also evaluated in terms of Appell functions to complete this study. Some special cases of the evaluated integrals yield some infinite series of generalized hypergeometric and Appell functions. As application, one of our main results is investigated to give an expression of the Generalized Humbert-Gaussian beams (GHGBs) propagating through a paraxial ABCD optical system.

Keywords

• integral transforms
• bessel functions
• humbert functions
• appell functions
• hypergeometric functions