Structural Formulas for Matrix-Valued Orthogonal Polynomials Related to $$2\times 2$$ Hypergeometric Operators

Abstract We give some structural formulas for the family of matrix-valued orthogonal polynomials size $$2\times 2$$ 2 × introduced by C. Calderón et al. in an earlier work, which are common eigenfunctions a differential operator hypergeometric type. Specifically, we Rodrigues formula that allows us to write this explicitly terms classical Jacobi polynomials, and write, sequence orthonormal three-term recurrence relation Christoffel–Darboux identity. obtain Pearson equation, enables prove derivatives is also orthogonal, compute these as well having eigenfunctions. describe second-order operators algebra associated with weight matrix.