The expected values of zonal polynomials of elliptically contoured distributions

Based on the work of Constantine, Waal, Shah, Khatri, and Muirhead, we have made further studies on the expected values of zonal polynomials and elementary symmetric functions of a Wishart matrix in this paper. Under certain conditions, we found the expected values of zonal polynomials and elementary symmetric functions of matrixXX, where the matrixX has matrix elliptically contoured distribution and obtain two interesting results. Three examples are given.