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Publishing Language: Chinese | Open Access

Irrationality measures of several types of irrational numbers

Zhibin LIANG( ), Yulun WANG
School of Mathematical Sciences, Capital Normal University, Beijing 100048
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Abstract

This paper uses generalized continued fractions to approximate e r , tan ⁡ ( r ) , tanh ⁡ ( r ) , r ∈ Q ∗ and shows that they are irrational numbers, and their irrationality measures are 2.

Keywords

generalized continued fractionsirrationality measureirrational number

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Journal of Capital Normal University (Natural Science Edition)
Volume 45 Issue 1,
February 2024
Pages 116-123
DOI: 10.19789/j.1004-9398.2024.01.011

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LIANG Z, WANG Y. Irrationality measures of several types of irrational numbers. Journal of Capital Normal University (Natural Science Edition), 2024, 45(1): 116-123. https://doi.org/10.19789/j.1004-9398.2024.01.011

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Received: 16 September 2023
Published: 01 February 2024
© The editorial department of Journal of Capital Normal University (Natural Science Edition) 2025.

This is an open access article under the CC BY-NC-ND 4.0 license (https://creativecommons.org/licenses/by-nc-nd/4.0/).