Matrix Gegenbauer Polynomials: The 2 × 2 Fundamental Cases

Abstract

In this paper, we exhibit explicitly a sequence of (Formula presented.) matrix valued orthogonal polynomials with respect to a weight (Formula presented.) , for any pair of real numbers p and n such that (Formula presented.). The entries of these polynomiales are expressed in terms of the Gegenbauer polynomials (Formula presented.). The corresponding three-term recursion relations are also given, and we make some studies of the algebra of differential operators associated with the weight (Formula presented.).