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In this paper, we derive explicit product formulas and positive convolutionstructures for three continuous classes of Heckman-Opdam hypergeometricfunctions of type $BC$. For specific discrete series of multiplicities thesehypergeometric functions occur as the spherical functions of non-compactGrassmann manifolds $G/K$ over one of the (skew) fields $\mathbb F= \mathbb R,\mathbb C, \mathbb H.$ We write the product formula of these sphericalfunctions in an explicit form which allows analytic continuation with respectto the parameters. In each of the three cases, we obtain a series of hypergroupalgebras which include the commutative convolution algebras of $K$-biinvariantfunctions on $G$.

Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC