## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  273.41012
Autor:  Erdös, Paul; Reddy, A.R.
Title:  A note on rational approximation. (In English)
Source:  Period. Math. Hung. 6, 241-244 (1975).
Review:  Let

\lambda0,n \equiv infp in \pin |{1 \over f(x)}-{1 \over p(x)} |Loo [0, oo),

where \pin denots the class of all polynomials of degree at most n. Then the authors prove the following. i) There is a sequence {g(n) } oon = 0 and an entire function f of infinite order so that for infinitely many n, \lambda0,n \leq l/g(n). (ii) Let f(z) = sum ook = 0akzk, a0 > 0, ak \geq 0, (k \geq 1) be an entire function of finite lower order \beta. Then for each \epsilon > 0,

limn ––> oo inf (\lambda0,n)1/n \leq \exp ({-1 \over (\beta+\epsilon)(e+1)} ).

Reviewer:  A.R.Reddy
Classif.:  * 41A20 Approximation by rational functions
41A50 Best approximation
41A25 Degree of approximation, etc.

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag