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arXiv · 1609.07076

Rational approximations of the exponential function at rational points

Kalle Leppälä·Tapani Matala-aho·Topi Törmä
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Abstract

We give explicit and asymptotic lower bounds for the quantity $|e^{s/t}-M/N|$ by studying a generalized continued fraction expansion of $e^{s/t}$. In cases $|s|\geq 3$ we improve existing results by extracting a large common factor from the numerators and the denominators of the convergents of that generalized continued fraction.

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Kalle Leppälä, Tapani Matala-aho, Topi Törmä. 2016-09-22. Rational approximations of the exponential function at rational points. https://arxiv.org/abs/1609.07076

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