Generalization of continued fractions. ІІ

Abstract

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 k Q n − P n Q k , where $ \frac{{{P_k}}}{{{Q_k}}} $ and $ \frac{{{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.