In this paper we present explicit product formulas for a continuous
two-parameter family of Heckman-Opdam hypergeometric functions of type BC on
Weyl chambers Cq⊂Rq of type B. These formulas are related
to continuous one-parameter families of probability-preserving convolution
structures on Cq×R. These convolutions on Cq×R
are constructed via product formulas for the spherical functions of the
symmetric spaces U(p,q)/(U(p)×SU(q)) and associated double coset
convolutions on Cq×T with the torus T. We shall
obtain positive product formulas for a restricted parameter set only, while the
associated convolutions are always norm-decreasing. Our paper is related to
recent positive product formulas of R\"osler for three series of Heckman-Opdam
hypergeometric functions of type BC as well as to classical product formulas
for Jacobi functions of Koornwinder and Trimeche for rank q=1