Deaño Cabrera, AlfredoKuijlaars, Arno B.J.Román, P.2023-12-212023-12-212023-06-15Advances in Mathematics, 423, 1090430001-8708https://hdl.handle.net/10016/39150We analyze the large degree asymptotic behavior of matrix valued orthogonal polynomials (MVOPs), with a weight that consists of a Jacobi scalar factor and a matrix part. Using the Riemann–Hilbert formulation for MVOPs and the Deift–Zhou method of steepest descent, we obtain asymptotic expansions for the MVOPs as the degree tends to infinity, in different regions of the complex plane (outside the interval of orthogonality, on the interval away from the endpoints and in neighborhoods of the endpoints), as well as for the matrix coefficients in the three-term recurrence relation for these MVOPs. The asymptotic analysis follows the work of Kuijlaars, McLaughlin, Van Assche and Vanlessen on scalar Jacobi-type orthogonal polynomials, but it also requires several different factorizations of the matrix part of the weight, in terms of eigenvalues/eigenvectors and using a matrix Szegő function. We illustrate the results with two main examples, MVOPs of Jacobi and Gegenbauer type, coming from group theory.61eng© 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Atribución-NoComercial-SinDerivadas 3.0 EspañaMatrix orthogonal polynomialsAsymptotic analysisRiemann-Hilbert problemsSteepest descent methodresearch articleMatemáticashttps://doi.org/10.1016/j.aim.2023.109043open access110904361Advances in mathematics423AR/0000033593