Some conjectures made by De Waal [Ann. Math. Statist. 43 (1972) 344-347] on the expectation of elementary symmetric functions of the roots of a noncentral Wishart matrix are proved true. The method of proof is through a simple, though perhaps obscure, property of these elementary symmetric functions and simple properties of the Wishart distribution.
"Expectation of Elementary Symmetric Functions of a Wishart Matrix." Ann. Statist. 1 (3) 580 - 582, May, 1973. https://doi.org/10.1214/aos/1176342428