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Limits of unbounded sequences of continued fractions

Published online by Cambridge University Press:  17 April 2009

Jingcheng Tong
Jingcheng Tong
Affiliation:
Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL 32216, United States of America
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Let X = {xk}k≥1 be a sequence of positive integers. Let Qk = [O;xk,xk−1,…,x1] be the finite continued fraction with partial quotients xi(1 ≤ i ≤ k). Denote the set of the limit points of the sequence {Qk}k≥1 by Λ(X). In this note a necessary and sufficient condition is given for Λ(X) to contain no rational numbers other than zero.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 3 , June 1990 , pp. 509 - 512
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Angell, D., ‘The limiting behaviour of certain sequences of continued fractions’, Bull. Austral. Math. Soc. 38 (1988), 67–76.CrossRefGoogle Scholar
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[3]Worley, R.T., ‘Estimating |α – p/q|’, J. Austral. Math. Soc. (Series A) 31 (1981), 202–206.CrossRefGoogle Scholar