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
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
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