# An integral transform and its application in the propagation of Lorentz-Gaussian beams

An integral transform and its application in the propagation of Lorentz-Gaussian beams AbstractThe aim of the present note is to derive an integral transform I=∫0∞xs+1e-βx2+γxMk,v(2ζx2)Jμ(χx)dx,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 by-product, 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 higher-order circular Lorentz-cosh-Gaussian beams through an ABCD optical system (see, for details [13], [3]). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematics de Gruyter

# An integral transform and its application in the propagation of Lorentz-Gaussian beams

, Volume 29 (3): 9 – Dec 1, 2021
9 pages

/lp/de-gruyter/an-integral-transform-and-its-application-in-the-propagation-of-8kHswtTtHd
Publisher
de Gruyter
eISSN
2336-1298
DOI
10.2478/cm-2021-0030
Publisher site
See Article on Publisher Site

### Abstract

AbstractThe aim of the present note is to derive an integral transform I=∫0∞xs+1e-βx2+γxMk,v(2ζx2)Jμ(χx)dx,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 by-product, 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 higher-order circular Lorentz-cosh-Gaussian beams through an ABCD optical system (see, for details [13], [3]).

### Journal

Communications in Mathematicsde Gruyter

Published: Dec 1, 2021

Keywords: Integral transform; Bessel function; Whittaker function; Confluent hypergeometric function; Lorentz-Gaussian beams; 33B15; 33C10; 33C15