On the convergence of periodic integral continued fractions with variable limits of integration

We establish estimates for the “tails” of periodic integral continued fractions with variable upper limits of integration. We prove a theorem on the uniform and absolute convergence of such fractions, and we obtain an estimate of their rate of convergence. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 28–34