Geodesic
On irrationality measure of some values of $\arctan \frac{1}{n}$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2020), pp. 32-40

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The aim of research is to obtain new estimates of extent of irrationality for a values $\arctan \frac{1}{5}, \arctan\frac{1}{3}.$ In this article we constructed new integral for getting irrationality measure of $\arctan \frac{1}{5}$, based on idea from work of K. Wu, 2002. We investigated linear form, generated by this integral and we found that it allow to get better estimate for this value. By the same method we constructed integral for obtaining an estimate of irrationality measure for $\arctan \frac{1}{3},$ and we also got new result for this value.
Keywords: irrationality measure, linear form. 
@article{IVM_2020_12_a3,
     author = {V. Kh. Salikhov and M. G. Bashmakova},
     title = {On irrationality measure of some values of $\arctan \frac{1}{n}$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {32--40},
     publisher = {mathdoc},
     number = {12},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_12_a3/}
}
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V. Kh. Salikhov; M. G. Bashmakova. On irrationality measure of some values of $\arctan \frac{1}{n}$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2020), pp. 32-40. http://geodesic.mathdoc.fr/item/IVM_2020_12_a3/