A matrix characterization for the ^Dν-semiclassical and ^Dν-coherent orthogonal polynomials

We present a new structure relation for the sequence of orthogonal polynomials associated with a ^Dν-semiclassical linear functional of class s, and then we use it to obtain a matrix characterization of the ^Dν-semiclassical orthogonal polynomials in terms of the Jacobi matrix associated with the multiplication operator in the basis of orthonormal polynomials, and the nonsingular lower triangular matrix that represents the orthogonal polynomials with respect to some bases of polynomials. We also provide a matrix characterization of ^Dν-coherent pairs of linear functionals.