  In this paper we consider the kernel of the radially deformed Fourier
transform introduced in the context of Clifford analysis in [10]. By adapting
the Laplace transform method from [4], we obtain the Laplace domain expressions
of the kernel for the cases of $m=2$ and $m > 2$ when $1+c=\frac{1}{n}, n\in
\mathbb{N}_0\backslash\{1\}$ with $n$ odd. Moreover, we show that the
expressions can be simplified using the Poisson kernel and the generating
function of the Gegenbauer polynomials. As a consequence, the inverse formulas
are used to get the integral expressions of the kernel in terms of
Mittag-Leffler functions.
