The noncentral means distribution for infinite error degrees of freedom and the noncentral Wishart distribution are derived as expansions in zonal polynomials. A method of calculating the zonal polynomials is outlined, and orthogonality properties of their coefficients stated.
"The Distribution of Noncentral Means with Known Covariance." Ann. Math. Statist. 32 (3) 874 - 882, September, 1961. https://doi.org/10.1214/aoms/1177704980