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We work out the expression of the generalized Bessel function of type B inthe two-rank case. This is done using Dijskma and Koornwinder's product formulafor Jacobi polynomials and the obtained expression is given by multipleintegrals involving only a normalized modified Bessel function and twosymmetric Beta distributions. We think of that expression as the major steptoward the explicit expression of the Dunkl's intertwining V operatorreflections-invariant functions. Finally, we give in the same setting anexplicit formula for the action of V on a product of a power of the norm and aspherical harmonic. The obtained formula extends to all dihedral systems and itimproves the one derived by Y.Xu.

Product formula for Jacobi polynomials, spherical harmonics and generalized Bessel function of dihedral type