Best uniform rational approximation of $x^α$ on $[0,1]$

dc.creatorStahl, Herbert
dc.date1993-01-01
dc.date.accessioned2026-07-07T09:14:52Z
dc.date.available2026-07-07T09:14:52Z
dc.descriptionA 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.description7 pages
dc.identifierhttps://arxiv.org/abs/math/9301217
dc.identifierhttp://arxiv.org/abs/math/9301217
dc.identifierBull. Amer. Math. Soc. (N.S.) 28 (1993) 116-122
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152831
dc.subjectClassical Analysis and ODEs
dc.titleBest uniform rational approximation of $x^α$ on $[0,1]$
dc.typetext

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