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

A_{n}(f) > e^{- \epsilon n} holds for infinitely many values of n, but if f(*Z*) is of 0 order then for every c > 0

A_{n}(f) > e^{-cn} holds for infinitely many n.

**Classif.: ** * 41A20 Approximation by rational functions

41A50 Best approximation

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