Abstract
We establish the conditions of existence and uniqueness of a multidimensional associated fraction with independent variables corresponding to a given formal multiple power series and deduce explicit relations for the coefficients of this fraction. The relationship between the multidimensional associated fraction and the multidimensional J-fraction with independent variables is demonstrated. The convergence of the multidimensional associated fraction with independent variables is investigated in some domains of the space ℂN. We construct the expansions of some functions into the corresponding two-dimensional associated fractions with independent variables and demonstrate the efficiency of approximation of the obtained expansions by convergents.
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