A matrix characterization for the D-v-semiclassical and D-v-coherent orthogonal polynomials Articles uri icon

publication date

  • December 2015

start page

  • 242

end page

  • 259

volume

  • 487

international standard serial number (ISSN)

  • 0024-3795

electronic international standard serial number (EISSN)

  • 1873-1856

abstract

  • We present a new structure relation for the sequence of orthogonal polynomials associated with a D-v-semiclassical linear functional of class s, and then we use it to obtain a matrix characterization of the D-v-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 D-v-coherent pairs of linear functionals.

keywords

  • semiclassical discrete orthogonal polynomials; matrix representation; structure relation; dν-coherent pairs