Approximation Results for alpha-Rosen Fractions
Cor Kraaikamp, Ionica Smeets
TL;DR
This paper extends classical approximation results to alpha-Rosen fractions, providing a geometric approach and analyzing conditions under which certain approximation constants hold.
Contribution
It generalizes Borel's approximation results to alpha-Rosen fractions and offers a geometric method for analyzing good approximations.
Findings
Generalization of Borel's results to alpha-Rosen fractions
Identification of conditions where Legendre constant exceeds Hurwitz constant
Geometric method for approximation analysis
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 give a Haas-Series-type result about all possible good approximations for the alpha for which the Legendre constant is larger than the Hurwitz constant.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Mathematical functions and polynomials · Advanced Mathematical Identities