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June 2009 A Diophantine Approximation of $e^{1/s}$ in Terms of Integrals
Tokyo J. Math. 32(1): 159-176 (June 2009). DOI: 10.3836/tjm/1249648415


Let $p_n/q_n$ be the $n$-th convergent of the continued fraction expansion of a real number $\alpha$. It is known that $|p_n-q_n\alpha|$ is very small tending to $0$ as $n$ tends to infinity. In this paper we establish a method how to express $p_n-q_n\alpha$ in terms of integrals when $\alpha$ is an $e$-type real number and its continued fraction expansion is quasi-periodic.


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Takao KOMATSU. "A Diophantine Approximation of $e^{1/s}$ in Terms of Integrals." Tokyo J. Math. 32 (1) 159 - 176, June 2009.


Published: June 2009
First available in Project Euclid: 7 August 2009

zbMATH: 1241.11076
MathSciNet: MR2541162
Digital Object Identifier: 10.3836/tjm/1249648415

Rights: Copyright © 2009 Publication Committee for the Tokyo Journal of Mathematics

Vol.32 • No. 1 • June 2009
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