Rational approximation on the nonnegative integers (Q1096819)

The author has previously proved that for f entire with positive Taylor coefficients there exist polynomials P of degree 2n such that \(| 1/f- 1/P| \leq 2/f(2n)\) uniformly over the natural numbers. [\textit{P. Erdős}, \textit{D. J. Newman}, and the author, J. Lond. Math. Soc. 15, 319-381 (1977; Zbl 0372.41008)]. He now gives downwards estimates for the degree of approximation of 1/f with rationals (uniformly over the natural numbers) in terms of order, type and lower type of f.