Development of the Theory of Branched Continued Fractions in 1996–2016

Resumo

We perform the analysis of investigations in the theory of branched continued fractions carried out for the last 20 years in the directions developed under the general supervision of Prof. V. Ya. Skorobohat’ko (18.07.1927–04.07.1996) including, in particular, the interpolation of functions of several variables by branched continued fractions, the determination of efficient criteria of convergence and computational stability of these fractions, the correspondence between multiple power series and functional branched continued fractions, the investigation of various classes of functional fractions, and the application of branched continued fractions.