Analysis. In particular are studied the properties of zonal polynomials, seen as spherical functions of a classical Gelfand … pair. A duality formula allows to write the zonal polynomials as spherical functions of a finite Gelfand pair. Finally a … combinatorial technique for the calculation of the zonal polynomials shows that these are the analogous, in the non-central Wishart …

The zonal polynomials are symmetric polynomial functions each of which is an eigenfunction of a kind of Laplace … coefficients of zonal polynomials. …

The generalized binomial coefficients (?[lambda]) are defined by , where the Ck(R) are the zonal polynomials of the m …