{"docId":9547,"paperId":9547,"url":"https:\/\/cm.episciences.org\/9547","doi":"10.2478\/cm-2021-0030","journalName":"Communications in Mathematics","issn":"1804-1388","eissn":"2336-1298","volume":[{"vid":649,"name":"Volume 29 (2021), Issue 3"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-03665031","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-03665031v1","dateSubmitted":"2022-05-11 15:43:01","dateAccepted":null,"datePublished":"2021-12-23 00:00:00","titles":{"en":"An integral transform and its application in the propagation of Lorentz-Gaussian beams"},"authors":["Belafhal, A.","Halba, E.M. El","Usman, T."],"abstracts":{"en":"The aim of the present note is to derive an integral transform I = \u222b 0 \u221e x s + 1 e - \u03b2 x 2 + \u03b3 x M k , v ( 2 \u03b6 x 2 ) J \u03bc ( \u03c7 x ) d x , I = \\int_0^\\infty {{x^{s + 1}}{e^{ - \\beta x}}^{2 + \\gamma x}{M_{k,v}}} \\left( {2\\zeta {x^2}} \\right)J\\mu \\left( {\\chi x} \\right)dx, involving the product of the Whittaker function Mk,\u03bd and the Bessel function of the first kind J\u00b5 of order \u00b5. As a by-product, we also derive certain new integral transforms as particular cases for some special values of the parameters k and \u03bd of the Whittaker function. Eventually, we show the application of the integral in the propagation of hollow higher-order circular Lorentz-cosh-Gaussian beams through an ABCD optical system (see, for details [13], [3])."},"keywords":[["General Mathematics"],"[MATH]Mathematics [math]"]}