Multivariate Meixner classes of invariant distributions

We define multivariate Meixner classes of invariant distributions of random matrices as those whose generating functions for the associated orthogonal polynomials are of certain special integral or summation forms, generalizing the univariate Meixner classes of distributions which were first characterized by Meixner 21]. Characterization theorems and properties of these multivariate Meixner classes are established. The zonal polynomials, the extended invariant polynomials with matrix arguments, and their related results in multivariate distribution theory are utilized in the discussion.