%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