On the convergence of branched continued fractions of a special Form in angular domains

Abstract

We study the angular domains of convergence of branched continued fractions of a special form with complex partial denominators. By using the sufficient criterion of convergence of these fractions with positive elements and the Stieltjes–Vitali theorem, we establish a many-dimensional analog of the van Vleck convergence criterion for continued fractions, as well as some other sufficient criteria of convergence under certain additional conditions imposed on the elements of fractions. The estimates of the rate of convergence for branched continued fractions of special form are obtained in these angular domains.