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

Author:
E. B. Saff

Journal:
Trans. Amer. Math. Soc. **153** (1971), 483-493

MSC:
Primary 30.70

MathSciNet review:
0274775

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Abstract: The object of the paper is to establish convergence throughout the entire complex plane of sequences of rational functions of prescribed types which satisfy a certain degree of approximation to the function on the disk . It is assumed that the approximating rational functions have a bounded number of free poles. Estimates are given for the degree of best approximation to the exponential function by rational functions of prescribed types. The results obtained in the paper imply that the successive rows of the Walsh array for on converge uniformly to on each bounded subset of the plane.

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DOI:
https://doi.org/10.1090/S0002-9947-1971-0274775-5

Keywords:
Free poles,
rational functions of type ,
best approximating rational functions,
Walsh array,
Padé table,
polynomial of least squares approximation,
generalized Bernstein lemma

Article copyright:
© Copyright 1971
American Mathematical Society