GENERALIZATION OF CONTINUED FRACTIONS. II

摘要

This work is a continuation of the study of recursive fractions begun in Mat. Metody Fiz.-Mekh. Polya, 54, No. 1, 57-64 (2011). We have constructed algorithms for calculating the value of the expression P_kQ_n-P_nQ_k, where P_k/Q_k and P_n/Q_n are the k th and n th rational truncations, respectively, of a certain recursive fraction. Using the values of this expression, we make some conclusions on the character and rate of convergence of rational truncations of a recursive fraction to its value.