  We work out the expression of the generalized Bessel function of type B in
the two-rank case. This is done using Dijskma and Koornwinder's product formula
for Jacobi polynomials and the obtained expression is given by multiple
integrals involving only a normalized modified Bessel function and two
symmetric Beta distributions. We think of that expression as the major step
toward the explicit expression of the Dunkl's intertwining V operator
reflections-invariant functions. Finally, we give in the same setting an
explicit formula for the action of V on a product of a power of the norm and a
spherical harmonic. The obtained formula extends to all dihedral systems and it
improves the one derived by Y.Xu.

Probability