Abstract
In this paper, the exact rate of decrease of best approximations of non-integer numbers by polynomials with integer coefficients is established.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
This manuscript has no associated data.
References
S. N. Bernstein, Sobranie sochineniy [Collected Works], Moscow, Akad. nauk SSSR, 1952 (Russian).
R. M. Trigub, Approximation of smooth functions and constants by polynomials with integer and natural coefficients, Mat. Zametki, 70 (2001), 123–136 (Russian). – English trans. in Math. Notes, 70 (2001), 110–122.
R. M. Trigub, On Chebyshev polynomials and integer coefficients, Mat. Zametki, 105 (2019), 302–312 (Russian). – English trans. in Math. Notes, 105 (2019), 291–300.
A. F. Timan, Theory of Approximation of Functions of a Real Variable, Fizmatgiz, Moscow, 1960 (Russian). – English transl.: Pergamon Press, MacMillan, N.Y. 1963 (there exist several later Dover publications of this translation).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Ethical conduct
Not applicable.
Conflict of interest
The author declares no competing interests.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Trigub, R.M. ON APPROXIMATION OF CONSTANTS BY POLYNOMIALS WITH INTEGER COEFFICIENTS. J Math Sci 266, 959–966 (2022). https://doi.org/10.1007/s10958-022-06244-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-022-06244-6