Multidimensional associated fractions with independent variables and multiple power series
AbstractWe 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.
How to Cite
Bodnar, D. I., and R. I. Dmytryshyn. “Multidimensional Associated Fractions With Independent variables and Multiple Power Series”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 3, Mar. 2019, pp. 325-49, https://umj.imath.kiev.ua/index.php/umj/article/view/1442.