Abstract

We construct determinantal expressions for the zonal spherical functions on the hyperboloids Hp,q = SO0(p, q; ?)/SO0(p - 1, q; ?) with p, q odd (and larger than 1). This gives rise to explicit evaluation formulas for hypergeometric series representing half-integer parameter families of Jacobi functions and (via specialization) Jacobi polynomials. © Springer-Verlag 2000.