Quantizations of Continued Fractions
A. Muhammed Uluda\u{g}, Esra \"Unal Yilmaz
TL;DR
This paper introduces a new four-parameter deformation of continued fractions, called U-deformation, and compares it with existing q-deformations, expanding the theoretical framework of continued fraction modifications.
Contribution
It presents a novel four-parameter deformation of continued fractions and analyzes its relation to existing q-deformations, broadening the understanding of continued fraction deformations.
Findings
Introduction of U-deformation of continued fractions
Comparison with q-deformation by Morier-Genoud and Ovsienko
Analysis of particular cases of the U-deformation
Abstract
We introduce a four-parameter deformation of continued fractions, which we call -deformation. We study some particular cases and compare them with the q-deformation of continued fractions introduce recently by Morier-Genoud and Ovsienko.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Mathematical Identities · Analytic Number Theory Research