Abstract
The purpose of this paper is to give conditions under which the absolute convergence of the subsequence of odd or of even approximants to a continued fraction implies convergence of the continued fraction. In § 2 we consider the problem in general, and in § 3 we impose a condition which gives absolute convergence of the odd or of the even part of the continued fraction and state conditions which imply convergence of the continued fraction.
Publisher
Canadian Mathematical Society
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Tests for the convergence of continued fractions, based on the fundamental system of inequalities;Mathematical Notes of the Academy of Sciences of the USSR;1976-11
2. Continued fractions with restricted variation properties;Annali di Matematica Pura ed Applicata;1975-12
3. The convergence of continued fractions;Mathematical Notes of the Academy of Sciences of the USSR;1967-03
4. Mathematical Notes;The American Mathematical Monthly;1962-12
5. A theorem on continued fractions and the fundamental inequalities;Proceedings of the American Mathematical Society;1962