Best uniform rational approximation of $x^α$ on $[0,1]$
| dc.creator | Stahl, Herbert | |
| dc.date | 1993-01-01 | |
| dc.date.accessioned | 2026-07-07T09:14:52Z | |
| dc.date.available | 2026-07-07T09:14:52Z | |
| dc.description | A strong error estimate for the uniform rational approximation of $x^α$ on $[0,1]$ is given, and its proof is sketched. Let $E_{nn}(x^α,[0,1])$ denote the minimal approximation error in the uniform norm. Then it is shown that $$\lim_{n\to\infty}e^{2π\sqrt{αn}}E_{nn}(x^α,[0,1]) = 4^{1+α}|\sinπα|$$ holds true for each $α>0$. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/9301217 | |
| dc.identifier | http://arxiv.org/abs/math/9301217 | |
| dc.identifier | Bull. Amer. Math. Soc. (N.S.) 28 (1993) 116-122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152831 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Best uniform rational approximation of $x^α$ on $[0,1]$ | |
| dc.type | text |