  In this paper, we develop a new method based on the Laplace transform to
study the Clifford-Fourier transform. First, the kernel of the Clifford-Fourier
transform in the Laplace domain is obtained. When the dimension is even, the
inverse Laplace transform may be computed and we obtain the explicit expression
for the kernel as a finite sum of Bessel functions. We equally obtain the plane
wave decomposition and find new integral representations for the kernel in all
dimensions. Finally we define and compute the formal generating function for
the even dimensional kernels.
