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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, Number 12, Pages 32–40
DOI: https://doi.org/10.26907/0021-3446-2020-12-32-40 (Mi ivm9633) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On irrationality measure of some values of $\arctan \frac{1}{n}$

V. Kh. Salikhov, M. G. Bashmakova

Bryansk State Technical University, 7 Blvd. 50-letiya Oktyabrya, Bryansk, 241035 Russia
Full-text PDF (386 kB) Citations (3)
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DOI: https://doi.org/10.26907/0021-3446-2020-12-32-40
Abstract: 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.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00296А
Received: 25.12.2019
Revised: 25.12.2019
Accepted: 01.10.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2020, Volume 64, Issue 12, Pages 29–37
DOI: https://doi.org/10.3103/S1066369X2012004X
Bibliographic databases:
Document Type: Article
UDC: 511.36
Language: Russian
Citation: V. Kh. Salikhov, M. G. Bashmakova, “On irrationality measure of some values of $\arctan \frac{1}{n}$”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 12, 32–40; Russian Math. (Iz. VUZ), 64:12 (2020), 29–37
Citation in format AMSBIB
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\paper On irrationality measure of some values of $\arctan \frac{1}{n}$
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2020
\issue 12
\pages 32--40
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\vol 64
\issue 12
\pages 29--37
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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