  In [M. R\"osler and M. Voit. Integral Representation and Uniform Limits for
Some Heckman-Opdam Hypergeometric Functions of type BC, Transactions of the
American Mathematical Society, Vol. 368, No. 8, 6005-6032, 2016.], R\"osler and
Voit give a formula for generalized spherical functions of type $BC$ in terms
of the spherical functions of type A. We use this formula to describe precisely
the support of the associated generalized Abel transform. Furthermore, we
derive a similar formula for the generalized spherical functions in the
rational Dunkl setting. The support of the intertwining operator V is also
deduced.
  We also show, as a consequence, that a Laplace-type expression exists for the
generalized spherical functions both in the trigonometric Dunkl setting and in
the rational Dunkl setting.
