Rational Approximation with Varying Weights III Original Research Article

Approximation by weighted rationals of the form wnrn, where rn=pn/qn, pn and qn are polynomials of degree at most [αn] and [βn], respectively, and w is an admissible weight, is investigated on compact subsets of the real line for a general class of weights and given α⩾0, β⩾0, with α+β>0. Conditions that characterize the largest sets on which such approximation is possible are given. We apply the general theorems to Laguerre and Freud weights.