Corpus ID: 119121285

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 $\frac{1}{\sqrt{k}}\arctg{\frac{1}{\sqrt{k}}}^1$
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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