Generalized Stieltjes polynomials and rational Gauss-Kronrod quadrature

17 pages, no figures.-- MSC1991 codes: Primary: 42C05, 41A20, 65D32; Secondary: 30E10.MR#: MR2036643 (2004m:33021)Zbl#: Zbl 1056.42017Generalized Stieltjes polynomials are introduced and their asymptotic properties outside the support of the measure are studied. As applications, we prove the convergence of sequences of interpolating rational functions, whose poles are partially fixed, to Markov functions and give an asymptotic estimate of the error of rational Gauss–Kronrod quadrature formulas when functions which are analytic on some neighborhood of the set of integration are considered.The work of M. Bello Hernández and B. de la Calle Ysern was partially supported by Dirección General de Enseñanza Superior (DGES) under grants BFM2000-0206-C04-03 and BFM2000-0206-C04-01, respectively. The work of G. López Lagomasino was partially supported by DGES under grant BFM2000-0206-C04-01 and by INTAS under grant 00-272.Publicad