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On Irrationality Measure of arctan \(\frac{1}{3}\)

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Abstract

We investigate the arithmetic properties of the value arctan \(\frac{1}{3}\). We elaborate special integral construction with the property of symmetry for evaluating irrationality measure of this number. We research linear form, generated by this integral, and prove a new result for extent of the irrationality of arctan \(\frac{1}{3}\), which improves the previous one.

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Acknowledgments

Supported by Russian Found of Fundamental Research, grant No. ‘18-01-00296A.

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

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Russian Text © V.Kh. Salikhov, M.G. Bashmakova, 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 1, pp. 69–75.

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Salikhov, V.K., Bashmakova, M.G. On Irrationality Measure of arctan \(\frac{1}{3}\). Russ Math. 63, 61–66 (2019). https://doi.org/10.3103/S1066369X19010079

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  • DOI: https://doi.org/10.3103/S1066369X19010079

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