CERTAIN HYPERGEOMETRIC-SERIES RELATED TO THE ROOT SYSTEM-BC

We show that the generalized hypergeometric function F-2(1) of matrix argument is the series expansion at the origin of a special case of th e hypergeometric function associated with the root system of type BC . In addition we prove that the Jacobi polynomials of matrix argument c orrespond to the Jacobi polynomials associated with the root system of type BC. We also give a precise relation between Jack polynomials and the Jacobi polynomials associated with the root system of type A . As a side result one obtains generalized hook-length formulas which are related to Harish-Chandra's c-function and one can prove a conjecture due to Macdonald relating two inner products on a space of symmetric f unctions.