On a confluent hypergeometric function of two variables

R. Garnier derived a system of partial differential equations called an N-dimensional Garnier system, which is a generalization of the sixth Painleve equation P-VI. The 2-dimensional Garnier system G(2) admits particular solutions expressed in terms of the Appell's hypergeometric function F-1 (alpha,beta,beta',gamma, x, y) and degenerate systems derived from G(2) also admit ones expressed in terms of confluent hypergeometric functions of two variables obtained from F-1 (alpha,beta,beta',gamma,x, y). In this paper we treat one of them, give a triple of linearly independent solutions of this system expanded into convergent series, and near the irregular singular locus x = infinity, examine the asymptotic behaviour of solutions.