on the zonal function and the faraut-koranyi hypergeometric function in rank two

In this paper we give a complete description of the generalized hypergeometric functions, introduced by faraut and kor’{a}nyi on the cartan domains. we establish some recursive relations with different arguments of zonal functions and some gauss type contiguous relations between the faraut-kor’{a}nyi hypergeometric functions on the domains of rank two. finally, we give an infinite sums involving classical hypergeometric functions.