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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.
Garza, L. G., Garza, L. E., Marcellán, F., & Pinzón-Cortés, N. C. (2015). A matrix characterization for the Dν-semiclassical and Dν-coherent orthogonal polynomials. Linear Algebra and Its Applications, 487, 242–259. https://doi.org/10.1016/j.laa.2015.09.014