Zentralblatt MATH

Publications of (and about) Paul Erdös
Zbl.No:  269.41014
Autor:  Erdös, Paul; Reddy, A.R.
Title:  Chebyshev rational approximation to entire functions. (In English)
Source:  Math. Struct., comput. Math., Math. Modelling (to appear). (1974).
Review:  Let f(Z) be an entire function with non-negative coefficients. Put

max max |{1 \over f(Z)}-{1 \over gn(Z)} | = An(f)

where the minimum is taken over all polynomials of degree not exceeding n. The authors obtain various inequalities for An(f) e.g. they prove that if f(Z) is of infinite order then for every \epsilon > 0

An(f) > e- \epsilon n

holds for infinitely many values of n, but if f(Z) is of 0 order then for every c > 0

An(f) > e-cn

holds for infinitely many n.
Classif.:  * 41A20 Approximation by rational functions
                   41A50 Best approximation

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