  In this study, we derive the exact distributions of eigenvalues of a singular
Wishart matrix under an elliptical model. We define generalized heterogeneous
hypergeometric functions with two matrix arguments and provide convergence
conditions for these functions. The joint density of eigenvalues and the
distribution function of the largest eigenvalue for a singular elliptical
Wishart matrix are represented by these functions. Numerical computations for
the distribution of the largest eigenvalue were conducted under the
matrix-variate $t$ and Kotz-type models.
