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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Polynomial approximation on $ y=x\sp{\alpha }$


Authors: E. Passow and L. Raymon
Journal: Proc. Amer. Math. Soc. 24 (1970), 781-783
MSC: Primary 41.41
DOI: https://doi.org/10.1090/S0002-9939-1970-0257624-5
MathSciNet review: 0257624
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Abstract: We show that on the curve $ y = {x^\alpha },\alpha $ any irrational, $ 0 \leqq x \leqq 1$, the degree of approximation by $ n$th degree polynomials in $ x$ and $ y$ in the $ {L^2}$ norm has order of magnitude $ 1/{n^{3/2}}$.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0257624-5
Article copyright: © Copyright 1970 American Mathematical Society