Mixed type Hermite–Padé approximants for Nikishin system

We consider a mixed type Hermite–Padé interpolation problem. We show that Nikishin systems are perfect with respect to this problem. Using the Gonchar–Rakhmanov vector equilibrium potential method we investigate the convergence of ray sequences of the approximants. We also discuss some algebraic properties of the Hermite–Padé polynomials: the interlacing of the zeros and the nearest neighbor recurrence relations.