The expected values of zonal polynomials of elliptically contoured distributions (Q804068)

The paper provides expressions for the expected values of zonal polynomials of matrix \(X'X\) in the case where X has a matrix elliptically contoured distribution. The work is based on results of similar nature provided by \textit{A. Constantine} [Ann. Math. Stat. 34, 1270-1285 (1963; Zbl 0123.368)], \textit{D. J. de Waal} [ibid. 43, 344-347 (1972; Zbl 0264.62017)], \textit{B. K. Shah} and \textit{C. G. Khatri} [Ann. Stat. 2, 833- 836 (1974; Zbl 0285.62026)], and \textit{R. J. Muirhead} [Aspects of multivariate statistical theory (New York, 1982)]. The examples that are provided include the multivariate t-distribution and the compound multivariate normal distribution. The fact that the expected values of the multivariate Cauchy distribution do not exist is an obvious consequence of the obtained results.