Mixed Type Hermite–Padé Approximants for a Nikishin System

We consider the problem of mixed type Hermite–Padé approximants and prove that the Nikishin system is perfect for this problem. Using the method of a vector equilibrium problem, we find weak asymptotics and prove the convergence of the approximants along any rays in the index table. We also present an equivalent statement in the form of a matrix Riemann–Hilbert problem.