Matrix Gegenbauer polynomials : the 2×2 fundamental cases
Abstract
In this paper, we exhibit explicitly a sequence of 2 × 2 matrix valued orthogonal polynomials
with respect to a weight W p,n , for any pair of real numbers p and n such that 0 < p < n. The entries of these polynomiales are expressed in terms of the Gegenbauer polynomials C k λ . Also the corresponding three-term recursion relations are given and we make some studies of the algebra of differential operators associated with the weight W p,n.