On the Van Vleck theorem for limit-periodic continued fractions of general form
Let \(A_1(z)/(B_1(z)+A_2(z)/(B_2(z)+ \cdots))\) be a continued fraction. Here the sequence of polynomials \(\{A_n\}_{n=1}^{\infty}\) has periodic limits with zeros lying on a finite set \(E\), and the sequence of polynomials \(\{B_n\}_{n=1}^{\infty}\) has periodic limits with zeros lying outside \(E\). The boundary of the convergence domain of the continued fraction is established. It is shown that the functions defined by continued fractions do not have a single-valued meromorphic continuation to any neighborhood of any nonisolated point of the boundary of the convergence set. The main theorem of the paper is a generalization of the Van Vleck theorem and Gonchar's complement to the Van Vleck theorem.
scientific article; zbMATH DE number 6844176
scientific article