Abstract: | Many multivariate non-null distributions and moment formulas can be expressed in terms of hypergeometric functions pFq of matrix arqument. Muirhead [6] and Constantine and Muirhead [2] gave partial differential equations for the functions of 2F1 of one argument matrix and two argument matrices, respectively. Such differential equations have been used to obtain asymptotic expansions of the functions (Muirhead [7], [8], [9], Sugiura [10]). The purpose of this paper is to derive partial differential equations for the functions 3F2 (a1 a2, a3; b1, b2, R) and 3F2 (a1, a2, a3; b1, b2; R, S). Differential equations for 2F2 are also obtained. |