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# On the irrationality measure of certain numbers

@article{Polyanskii2015OnTI,
title={On the irrationality measure of certain numbers},
author={A. Polyanskii},
journal={arXiv: Number Theory},
year={2015}
}
The paper presents upper estimates for the irrationality measure and the non-quadraticity measure for the numbers $\alpha_k=\sqrt{2k+1}\ln\frac{\sqrt{2k+1}-1}{\sqrt{2k+1}+1}, \ k\in\mathbb N.$
2 Citations
On the Irrationality Measures of Certain Numbers. II
For the irrationalitymeasures of the numbers $$\sqrt {2k - 1}$$2k−1 arctan$$\left( {\sqrt {2k - 1} /\left( {k - 1} \right)} \right)$$(2k−1/(k−1)), where k is an even positive integer, upper boundsExpand
Об оценке меры иррациональности чисел вида $\sqrt{4k+3}\ln{\frac{\sqrt{4k+3}+1}{\sqrt{4k+3}-1}}$ и $\frac{1}{\sqrt{k}}\arctg{\frac{1}{\sqrt{k}}}^1$
• Mathematics
• 2018
The arithmetic properties of the values of hypergeometric function have been studied by various methods since the paper of C. Siegel in 1929. This direction of the theory of DiophantineExpand

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