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.
Acknowledgements
The work of the first author is partially supported by MCI ref. MTM2009-12740-C03-02, FQM-262, FQM-4643 (Junta de Andalucía). This work was prepared during the visit of the second author to the University of Seville.