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Proceedings of the American Mathematical Society
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
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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?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0430222-2
PII: S 0002-9939(1977)0430222-2
Keywords: Continued fractions, convergence regions for continued fractions, value regions for continued fractions
Article copyright: © Copyright 1977 American Mathematical Society