Dmytryshyn R. I.
Ukr. Mat. Zh. - 2019. - 71, № 3. - pp. 325-349
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.
Ukr. Mat. Zh. - 2014. - 66, № 9. - pp. 1175–1184
An algorithm for the expansion of a given formal double power series in the associated branched continued fraction with two independent variables is constructed and the conditions for the existence of this expansion are established.