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The invariant differential operators are applied to derive partial differential equations for the zonal polynomials, to calculate generalized binomial coefficients and certain multivariate integrals, and to deduce a characterization of EP functions (Kushner, Lebow and Meisner, J. Multivariate Anal., 11 (1981), pp. 418–433).

Applications of Invariant Differential Operators to Multivariate Distribution Theory