Rates of Best Rational Approximation of Analytic Functions

Let E be a compact set in the extended complex plane C and let f be holomorphic on E. Denote by ρn the distance from f to the class of all rational functions of order at most n, measured with respect to the uniform norm on E. We obtain results characterizing the relationship between estimates of lim infn→∞ ρ1/nn and lim supn→∞ ρ1/nn.