 Then the hypergeometric function of a matrix argument formula_5
and parameter formula_6 is defined as

where formula_8 means formula_9 is a partition of formula_10, formula_11 is the Generalized Pochhammer symbol, and 
formula_12 is the "C" normalization of the Jack function.If formula_5 and formula_14 are two formula_4 complex symmetric matrices, then the hypergeometric function of two matrix arguments is defined as