Abstract: In this paper, we compute the Bergman kernel function on W_III.and RIII(q) denote the Cartan domain of the third class. Because domain W_III is neither homogeneous domain nor Reinhardt domain, we will use a new way to solve this problem. First, we give a holomorphic automorphism group, such that for any Zo, there exists an element of this group, which maps (W, Zo) into (W,O). Second, introduce the concept of semi-Reinhardt and discuss the complete orthonormal system of this domain.

Key words: Bergman , kernel , function, holomorphic , automorphism , group, complete , or- thonormal system