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Proceedings of the American Mathematical Society

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

 

 

The convergence of rational functions of best approximation to the exponential function. II


Author: E. B. Saff
Journal: Proc. Amer. Math. Soc. 32 (1972), 187-194
MSC: Primary 30A82
MathSciNet review: 0294656
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Abstract: Let $ {W_{m,n}}(z)$ be a rational function of type (m, n) of best uniform approximation to the function $ {e^z}$ on the closed unit disk. In this paper we show that any sequence $ \{ {W_{m,n}}(z)\} $ for which $ m + n \to \infty $ must converge to $ {e^z}$ for all values of z. This is the first result which describes completely the regions of convergence of arbitrary sequences formed from a Walsh array.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0294656-7
Keywords: Best uniform approximation, rational functions of type (m, n), Walsh array, Padé table, Bernstein lemma, Taylor development, polynomial of least squares approximation
Article copyright: © Copyright 1972 American Mathematical Society