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