June 2024 Algorithms of Transformation between Positive and Even Continued Fractions
Yoshinori JIBIKI
Tokyo J. Math. 47(1): 111-123 (June 2024). DOI: 10.3836/tjm/1502179397

Abstract

Any rational number $r$ can be represented uniquely by a finite positive (resp. even) continued fraction in an essentially unique way. Thus positive continued fractions uniquely correspond to even continued fractions. In this paper, we give Algorithm PtoE and Algorithm EtoP ; Algorithm PtoE directly transforms positive continued fractions into even continued fractions and Algorithm EtoP directly transforms even continued fractions into positive continued fractions without knowing the value of them. These algorithms can be applied to infinite positive and even continued fractions, too. As an application, we give the even continued fraction expansions of $e$ and $\sqrt{e}$, where $e$ is Napier's constant.

Citation

Download Citation

Yoshinori JIBIKI. "Algorithms of Transformation between Positive and Even Continued Fractions." Tokyo J. Math. 47 (1) 111 - 123, June 2024. https://doi.org/10.3836/tjm/1502179397

Information

Published: June 2024
First available in Project Euclid: 19 August 2024

Digital Object Identifier: 10.3836/tjm/1502179397

Subjects:
Primary: 11A55
Secondary: 11J70 , 11Y65

Rights: Copyright © 2024 Publication Committee for the Tokyo Journal of Mathematics

Vol.47 • No. 1 • June 2024
Back to Top