Abstract
We produce an (N+2)-parametric family of matrix polynomials (P n ) n of size N×N, which are orthogonal with respect to a weight matrix, involving classical Laguerre scalar weights associated with different exponential functions. This family of orthogonal matrix polynomials satisfies a second-order differential equation with differential coefficients (independent of n) that are matrix polynomials F 2, F 1, and F 0 of degree not larger than 2, 1 and 0, respectively. To proceed in depth, we deal with the particular size 2×2. The Rodrigues formula is obtained to provide an explicit expression as well as the three-term recurrence relation for the referred family of polynomials. As a consequence of the weight's structure, these recurrence coefficients do not behave asymptotically as multiples of the identity.
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