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# Approximation results for $\alpha$-Rosen fractions

Author(s): Cor Kraaikamp | Ionica Smeets

Journal: Uniform Distribution Theory
ISSN 1336-913X

Volume: 5;
Issue: 2;
Start page: 15;
Date: 2010;

Keywords: Rosen fractions | natural extensions | approximation quality

ABSTRACT
In this article we generalize Borel's classical approximation results for the regular continued fraction expansion to the $\alpha$-Rosen fraction expansion, using a geometric method. We use $\alpha$-Rosen fractions to give a Haas-Series-typeresult about all possible good approximations for the $\alpha$ for which the Legendre constant is larger than the Hurwitz constant.