Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Boundedness of value regions and convergence of continued fractions

Author: F. A. Roach
Journal: Proc. Amer. Math. Soc. 62 (1977), 299-304
MSC: Primary 30A22; Secondary 40A15
MathSciNet review: 0430222
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: If the elements of a continued fraction are restricted to lie within some region E of the complex plane, it is quite often possible to determine, with very little difficulty, where the approximants of the continued fraction lie. Generally, it is more difficult to determine whether every continued fraction with elements from this set E is convergent. In this paper, we give some results which, in certain cases, reduce the question of convergence to the question of whether the set of approximants is bounded.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A22, 40A15

Retrieve articles in all journals with MSC: 30A22, 40A15

Additional Information

Keywords: Continued fractions, convergence regions for continued fractions, value regions for continued fractions
Article copyright: © Copyright 1977 American Mathematical Society