The two-dimensional gg-fraction with independent variables for double power series

In this paper the two-dimensional gg-fraction with independent variables which is the generalization of the continued gg-fraction is considered. The correspondence between the formal double power series and the above mentioned fraction is studied. As a result the algorithm for the expansion of the formal double power series into the corresponding two-dimensional gg-fraction with independent variables has been constructed and the conditions for the existence of such an algorithm have been established. The expansion of some functions into the corresponding two-dimensional gg-fraction with independent variables is constructed and the efficiency of the obtained expansion by using approximants is shown.