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Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

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

Author(s): Herbert Stahl
Journal: Bull. Amer. Math. Soc. 28 (1993), 116-122.
MathSciNet review: 1168517
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Abstract | References | Additional information

Abstract: 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

$\displaystyle \mathop {\lim }\limits_{x \to \infty } {e^{2\pi \sqrt {\alpha n} }}{E_{nn}}({x^\alpha },[0,1]) = {4^{1 + \alpha }}\vert\sin \pi \alpha \vert$

holds true for each $ {\alpha > 0}$.

References:

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Additional Information:

DOI: 10.1090/S0273-0979-1993-00351-3
PII: S 0273-0979(1993)00351-3
Copyright of article: Copyright 1993, American Mathematical Society




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