Convergence of Multidimensional A- and J-Fractions with Independent Variables

Abstract

The paper deals with the problem of convergence of special classes of branched continued fractions including the multidimensional A- and J-fractions with independent variables, which are generalizations of A-fractions (associated fractions) and J-fractions (Jakobi’s fractions), respectively. These branched continued fractions are used for the approximation of analytic functions of several complex variables. We have used a research method is to extend convergence, already known for a small domain, to a larger domain. As a result, we have established some new convergence criteria for the above mentioned branched continued fractions.