Matrix Orthogonal Polynomials: A Riemann--Hilbert approach

In this work we show how to get advantage from the Riemann–Hilbert analysis in order to obtain information about the matrix orthogonal polynomials and functions of second kind associated with a weight matrix. We deduce properties for the recurrence relation coefficients from differential properties of the weight matrix. We take the matrix polynomials of Hermite, Laguerre and Jacobi type as a case study.