Hypergeometric functions of matrix arguments occur frequently in multivariate statistical analysis. In this paper, we define and study extended forms of Gauss and confluent hypergeometric functions of matrix arguments and show that they occur naturally in statistical distribution theory.

We study several properties of matrix variate beta type 3 distribution. We also derive probability density functions of the product of two independent random matrices when one of them is beta type 3. These densities are expressed in terms of Appell′s first hypergeometric function F₁ and Humbert′s confluent hypergeometric function Φ₁ of matrix arguments. Further, a bimatrix variate generalization of the beta type 3 distribution is also defined and studied.

In this article, we study several properties of extended Gauss hypergeometric and extended confluent hypergeometric functions. We derive several integrals, inequalities and establish relationship between these and other special functions. We also show that these functions occur naturally instatistical distribution theory.

A new bimatrix variate beta type 1 distribution is introduced and several of its properties are studied.