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The closure of convergence sets for continued fractions are convergence sets
Published online by Cambridge University Press: 20 January 2009
Abstract
We prove that if Ω is a simple convergence set for continued fractions K(an/bn), then the closure of Ω is also such a convergence set. Actually, we prove more: every continued fraction K(an/bn) has a “neighbourhood” where rn>0 and sn>0, with the following property: Every continued fraction from {n} converges if and only if K(an/bn) converges.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 37 , Issue 1 , February 1994 , pp. 39 - 46
- Copyright
- Copyright © Edinburgh Mathematical Society 1994
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