Representation of a quotient of solutions of a four-term linear recurrence relation in the form of a branched continued fraction

Abstract

An analysis of the research in the theory of branched continued fractions over the past 20 years in directions evolved under the general guidance of Professor V. Ya. Skorobogatko (18.07.1927 – 04.07.1996), namely: interpolation of functions of several variables by branched continued fractions, the establishment of effective tests of convergence and computational stability of such fractions, correspondence between multiple power series and functional branched continued fractions, the study of various classes of functional fractions, and applications of branched continued fractions is done.