@article{Bodnar_Dmytryshyn_2019, title={Multidimensional associated fractions with independent variables
and multiple power series}, volume={71}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/1442}, abstractNote={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.}, number={3}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Bodnar, D. I. and Dmytryshyn, R. I.}, year={2019}, month={Mar.}, pages={325-349} }