Parabolic convergence regions of branched continued fractions of the special form

Using the criterion of convergence of branched continued fractions of the special form with positive elements, effective sufficient criteria of convergence for these fractions are established. To study the parabolic regions of convergence, the element regions and value regions technique was used. In particular, half-planes are considered as value regions. A multidimensional analogue of Tron's twin convergence regions for branched continued fractions of the special form is established. The obtained results made it possible to establish the conditions for the convergence of the multidimensional S-fractions with independent variables.

Automated summary

Effective criteria of convergence for branched continued fractions of special form with positive elements were established using the criterion of convergence. The study of parabolic regions of convergence utilized the technique of element regions and value regions, with half-planes considered as value regions. A multidimensional analogue of Tron's twin convergence regions for branched continued fractions of the special form was established, providing conditions for the convergence of multidimensional S-fractions with independent variables.