# On Irrationality Measure of arctan $$\frac{1}{3}$$13

@article{Salikhov2019OnIM,
title={On Irrationality Measure of arctan \$\$\frac\{1\}\{3\}\$\$13},
author={V. Salikhov and M. Bashmakova},
journal={Russian Mathematics},
year={2019},
volume={63},
pages={61-66}
}
• Published 2019
• Mathematics
• Russian Mathematics
We investigate the arithmetic properties of the value arctan $$\frac{1}{3}$$13. 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 $$\frac{1}{3}$$13, which improves the previous one.
1 Citations

#### References

SHOWING 1-9 OF 9 REFERENCES
On the irrationality measure of log3
• Mathematics
• 2014
Abstract In this paper, we obtain a new estimate of an irrationality measure of the number log 3 . We have μ ( log 3 ) ≤ 5.1163051 with an “arithmetical method”. The previous results were μ ( log 3 )Expand
On the linear independence measure of logarithms of rational numbers
• Qiang Wu
• Mathematics, Computer Science
• Math. Comput.
• 2003
A general theorem is given on the linear independence measure of logarithms of rational numbers and, in particular, the linearindependence measure of 1, log 2, log 3, log 5 and of 2, 3, 4 and 5. Expand
On irrationality measures of the values of Gauss hypergeometric function
• Mathematics
• 1993
The paper gives irrationality measures for the values of some Gauss hypergeometric functions both in the archimedean andp-adic case. Further, an improvement of general results is obtained in the caseExpand
An application of Jacobi type polynomials to irrationality measures
• Mathematics
• 1994
The paper provides irrationality measures for certain values of binomial functions and definite integrals of some rational functions. The results are obtained using Jacobi type polynomials andExpand
Irrationalité de certaines integrales hypergéométriques
Resume Dans cet article nous appliquons la theorie des approximants de Pade a l'etude des approximations diophantiennes des integrales hypergeometriques 2 F 1 1, 1 k 1+ 1 k ϵx k , pour k entier ≥ 2Expand