Open AccessOn the convergence criterion for branched continued fractions with independent variables
Author(s) -
R. I. Dmytryshyn
Publication year - 2018
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.9.2.120-127
Subject(s) - mathematics , convergence (economics) , generalization , fraction (chemistry) , multivariable calculus , series (stratigraphy) , domain (mathematical analysis) , type (biology) , partial fraction decomposition , power series , pure mathematics , mathematical analysis , paleontology , ecology , chemistry , rational function , organic chemistry , control engineering , engineering , economics , biology , economic growth
In this paper, we consider the problem of convergence of an important type of multidimensional generalization of continued fractions, the branched continued fractions with independent variables. These fractions are an efficient apparatus for the approximation of multivariable functions, which are represented by multiple power series. We have established the effective criterion of absolute convergence of branched continued fractions of the special form in the case when the partial numerators are complex numbers and partial denominators are equal to one. This result is a multidimensional analog of the Worpitzky's criterion for continued fractions. We have investigated the polycircular domain of uniform convergence for multidimensional C-fractions with independent variables in the case of nonnegative coefficients of this fraction.