New properties of a continuant has been proved. Using the relationship between the continuant and the continued fraction, an estimate of the remainder term of Thiele’s interpolation continued fraction is obtained.

We prove that the polynomials of canonical numerators and denominators of the interpolation and approximation convergents of Thiele's continued fractions have no common zeros. It is shown that the convergents of Thiele's ...

Let function u(z, w) = f(z)h(w) be defined on the comp. We study the problem of representation of functions of this class by the product of two continued fractions, which is called a bicontinued fraction. Some properties ...