Generalized Hermite-Padé approximation for Nikishin systems of three functions

9 pages, no figures.-- MSC1991 code: Primary 42C05.-- Issue title: "Special Functions, Information Theory, and Mathematical Physics". Special issue dedicated to Professor Jesús Sánchez Dehesa on the occasion of his 60th birthday.Zbl#: Zbl pre05650072Nikishin systems of three functions are considered. For such systems, the rate of convergence of simultaneous interpolating rational approximations with partially prescribed poles is studied. The solution is described in terms of the solution of a vector equilibrium problem in the presence of a vector external field.First author’s research supported by grants MTM 2006-13000-C03-02 from Ministerio de Ciencia y Tecnología and CCG 06–UC3M/ESP–0690 of Universidad Carlos III de Madrid-Comunidad de Madrid and by grant SFRH/BPD/31724/2006 from Fundação para a Ciência e a Tecnologia. Second author’s research supported by grants MTM 2006-13000-C03-02 from Ministerio de Ciencia y Tecnología and CCG 06–UC3M/ESP–0690 of Universidad Carlos III de Madrid-Comunidad de Madrid.Publicad