Multidimensional associated fractions with independent variables and multiple power series - Bodnar, D. I.; Dmytryshyn, R. I. (Ukrains’kyi Matematychnyi Zhurnal, 2019)
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 C^N. The expansions of some functions into the corresponding two-dimensional associated fraction with independent variables are constructed and the efficiency of approaching of the obtained expansions by approximants is shown.