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This paper discusses certain properties of heterogeneous hypergeometricfunctions with two matrix arguments. These functions are newly defined but havealready appeared in statistical literature and are useful when dealing with thederivation of certain distributions for the eigenvalues of singularbeta-Wishart matrices. The joint density function of the eigenvalues and thedistribution of the largest eigenvalue can be expressed in terms of certainheterogeneous hypergeometric functions. Exact computation of the distributionof the largest eigenvalue is conducted here for a real case.

Heterogeneous hypergeometric functions with two matrix arguments and the  exact distribution of the largest eigenvalue of a singular beta-Wishart  matrix