The Usual Behavior of Rational Approximation, II Original Research Article

The speeds of convergence of best rational approximations, best polynomial approximations, and the modulus of continuity on the unit disc are compared. We show that, in a Baire category sense, it is expected that subsequences of these approximants will converge at the same rate. Similar problems on the interval [−1, 1] are also examined. A problem raised by P. Turán (J. Approx. Theory29, 1980, 23-89) concerning rational approximation to non-analytically continuable ƒ on the unit circle is negated as an application.