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On Irrationality Measure of Some Values of \(\operatorname{arctg} \frac{1}{n}\)

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Abstract

The aim of research is to obtain new estimates of extent of irrationality for values \(\arctan \frac{1}{5}, \arctan\frac{1}{3}.\) In this article, we constructed a new integral for getting an irrationality measure of \(\arctan \frac{1}{5}\) based on the idea from work of K. Wu, 2002. We investigated the linear form generated by this integral and found that it allows to get a better estimate for this value. By the same method, we constructed an integral for obtaining an estimate of irrationality measure for \(\arctan \frac{1}{3},\) and we also got a new result for this value.

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Funding

The work was supported by Russian Foundation for Basic Research, grant no. 18-01-00296A.

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Authors and Affiliations

  1. Bryansk State Technical University, 7 Blvd. 50- letiya Oktyabrya, 241035, Bryansk, Russia

    V. Kh. Salikhov & M. G. Bashmakova

Authors
  1. V. Kh. Salikhov
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  2. M. G. Bashmakova
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Corresponding authors

Correspondence to V. Kh. Salikhov or M. G. Bashmakova.

Additional information

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 12, pp. 32–40.

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Salikhov, V.K., Bashmakova, M.G. On Irrationality Measure of Some Values of \(\operatorname{arctg} \frac{1}{n}\). Russ Math. 64, 29–37 (2020). https://doi.org/10.3103/S1066369X2012004X

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  • DOI: https://doi.org/10.3103/S1066369X2012004X

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