Three-Dimensional Generalization of Corresponding Regular C-Fraction

We consider one type of functional three-dimensional continued fractions corresponding to formal triple power series, namely, the so-called three-dimensional regular C-fractions. By using the tails of a threedimensional regular C-fraction, the formula for the difference between two approximants of the threedimensional regular C -fraction in terms of these tails, and the correspondence principle, we study the properties of these fractions. As the main results, we can mention the proof of uniqueness and convergence of the formal triple power series corresponding to a three-dimensional regular C -fraction.