Hypergeometric function of a matrix argument

Summary

A hypergeometric function of a matrix argument ${}_pF_q^{(\alpha)}(a; b; X)$ is a generalisation of the generalized hypergeometric function in which the variable is a matrix $X$. The series runs over integer partitions. The powers $z^k$ are replaced by Jack polynomials in the eigenvalues of $X$, and the rising factorials by generalized Pochhammer symbols. These functions appear in multivariate statistics and random matrix theory, where densities of eigenvalues of Wishart and related matrices are written with them.