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Approximation of the function $|x|$ by rational functions

N. S. Vyacheslavov

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 517.5

Received: 12.08.1973

 English version: Mathematical Notes, 1974, 16:1, 680–685

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