Convergence criteria for branched continued fractions with nonnegative components

For branched continued fractions with nonnegative components and a fixed or variable number of branchings we establish necessary and sufficient conditions for their approximants to be well-defined. We study necessary and sufficient conditions for convergence that are multivariable analogs of the known Seidel-Stern and Stern criteria for continued fractions with positive elements. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 7–13.