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In this paper, we derive a Laplace-type integral representations for both thegeneralized Bessel function and the Dunkl kernel associated with the rank-tworoot system of type B_2. The derivation of the first one elaborates on theintegral representation of the generalized Bessel function proved in\cite{Demni} through the modified Bessel function of the first kind. Inparticular, we recover an expression of the density of the Duistermaat-Heckmanmeasure for the dihedral group of order eight. As to the integralrepresentation of the corresponding Dunkl kernel, it follows from anapplication of the shift principle to the generalized Bessel function.

Laplace-type integral representations of the generalized Bessel function and of the Dunkl kernel of type $B_2$