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

DOI:
https://doi.org/10.1090/S0002-9939-1972-0294656-7

MathSciNet review:
0294656

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a rational function of type (*m, n*) of best uniform approximation to the function on the closed unit disk. In this paper we show that any sequence for which must converge to 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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Additional Information

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