Calculation of Zonal Polynomial Coefficients by Use of the Laplace-Beltrami Operator
Open Access
- 1 October 1968
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Mathematical Statistics
- Vol. 39 (5) , 1711-1718
- https://doi.org/10.1214/aoms/1177698153
Abstract
The zonal polynomials of the positive definite real symmetric matrices, which appear in the expansions of the functions occurring in many multivariate non null distributions and moment formulae are eigenfunctions of the Laplace Beltrami operator. The resulting differential equation gives a recurrence relation between the coefficients from which they can be calculated.Keywords
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