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

AIMS Mathematics

A. Belafhal¹  L. Dalil-Essakali¹  N. Nossir¹  T. Usman² 

[1] 1 LPNAMME, Laser Physics Group, Department of Physics, Faculty of Sciences, Chouaïb Doukkali University, P. B 20, 24000 El Jadida, Morocco;2 Department of Mathematics, School of Basic and Applied Sciences, Lingaya’s Vidyapeeth, Faridabad-121002, Haryana, India;

关键词: integral transforms;    bessel functions;    humbert functions;    appell functions;    hypergeometric functions;   

DOI  :  10.3934/math.2020086

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown