%0 Journal Article
%T Best uniform rational approximation of $x^¦Á$ on $[0,1]$
%A Herbert Stahl
%J Mathematics
%D 1993
%I arXiv
%X A strong error estimate for the uniform rational approximation of $x^\alpha$ on $[0,1]$ is given, and its proof is sketched. Let $E_{nn}(x^\alpha,[0,1])$ denote the minimal approximation error in the uniform norm. Then it is shown that $$\lim_{n\to\infty}e^{2\pi\sqrt{\alpha n}}E_{nn}(x^\alpha,[0,1]) = 4^{1+\alpha}|\sin\pi\alpha|$$ holds true for each $\alpha>0$.
%U http://arxiv.org/abs/math/9301217v1