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 variablescorresponding 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 independentvariables is demonstrated. The convergence of the multidimensional associated fraction with independent variables isinvestigated in some domains of the space $C^N$. The expansions of some functions into the corresponding two-dimensionalassociated fraction with independent variables are constructed and the efficiency of approaching of the obtained expansionsby approximants is shown.