Matematičeskie zametki, Tome 16 (1974) no. 1, pp. 163-171
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N. S. Vyacheslavov. Approximation of the function $|x|$ by rational functions. Matematičeskie zametki, Tome 16 (1974) no. 1, pp. 163-171. http://geodesic.mathdoc.fr/item/MZM_1974_16_1_a18/
@article{MZM_1974_16_1_a18,
author = {N. S. Vyacheslavov},
title = {Approximation of the function $|x|$ by rational functions},
journal = {Matemati\v{c}eskie zametki},
pages = {163--171},
year = {1974},
volume = {16},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_1_a18/}
}
TY - JOUR
AU - N. S. Vyacheslavov
TI - Approximation of the function $|x|$ by rational functions
JO - Matematičeskie zametki
PY - 1974
SP - 163
EP - 171
VL - 16
IS - 1
UR - http://geodesic.mathdoc.fr/item/MZM_1974_16_1_a18/
LA - ru
ID - MZM_1974_16_1_a18
ER -
%0 Journal Article
%A N. S. Vyacheslavov
%T Approximation of the function $|x|$ by rational functions
%J Matematičeskie zametki
%D 1974
%P 163-171
%V 16
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1974_16_1_a18/
%G ru
%F MZM_1974_16_1_a18
We consider the problem of the approximation of the function $|x|$ by rational functions. We make more precise the best approximation estimate obtained by A. P. Bulanov. We prove that for arbitrary positive integral $n$$$ R_n[|x|]<Ane^{-\pi\sqrt n} $$ where $A$ is an absolute constant.
