TY - JOUR
AU - D. I. Bodnar
AU - R. I. Dmytryshyn
PY - 2019/03/25
Y2 - 2022/09/26
TI - Multidimensional associated fractions with independent variables
and multiple power series
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 71
IS - 3
SE - Research articles
DO -
UR - http://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 -