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The aim of the present note is to derive an integral transform $$I={\int }_0^{\infty }{x}^{s+1}{e}^{-\beta x^2+\gamma x}{M}_{k,\nu }\left(2\zeta x^2\right)J_{\mu }\left(\chi x\right)dx,$$ involving the product of the Whittaker function $M_{k,\nu }$ and the Bessel function of the first kind $J_{\mu }$ of order $\mu$. As a by-product, we also derive certain new integral transforms as particular cases for some special values of the parameters $k$ and $\nu$ 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,...