episciences.org_9547_1669864125
1669864125
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Communications in Mathematics
23361298
12
23
2021
Volume 29 (2021), Issue 3
An integral transform and its application in the propagation of LorentzGaussian beams
A.
Belafhal
E.M. El
Halba
T.
Usman
The aim of the present note is to derive an integral transform I = ∫ 0 ∞ x s + 1 e  β x 2 + γ x M k , v ( 2 ζ x 2 ) J μ ( χ 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,ν and the Bessel function of the first kind Jµ of order µ. As a byproduct, we also derive certain new integral transforms as particular cases for some special values of the parameters k and ν of the Whittaker function. Eventually, we show the application of the integral in the propagation of hollow higherorder circular LorentzcoshGaussian beams through an ABCD optical system (see, for details [13], [3]).
12
23
2021
9547
https://creativecommons.org/licenses/byncn
https://hal.archivesouvertes.fr/hal03665031v1
10.2478/cm20210030
https://cm.episciences.org/9547

https://cm.episciences.org/9547/pdf