ASYMPTOTICS FOR STIELTJES POLYNOMIALS, PADÉ-TYPE APPROXIMANTS, AND GAUSS-KRONROD QUADRATURE

Abstract. We study the asymptotic properties of Stieltjes polynomials outside the sup-port of the measure as well as the asymptotic behaviour of their zeros. These properties are used to estimate the rate of convergence of sequences of rational functions, whose poles are partially fixed, which approximate Markov-type functions. An estimate for the speed of convergence of Gauss-Kronrod quadrature formula in the case of analytic functions is also given. 1