TY - JOUR AU - D. I. Bodnar AU - R. I. Dmytryshyn PY - 2019/03/25 Y2 - 2024/03/29 TI - Multidimensional associated fractions with independent variables and multiple power series JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 71 IS - 3 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1442 AB - 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. ER -