A matrix approach for the semiclassical and coherent orthogonal polynomials Articles uri icon

publication date

  • April 2015

start page

  • 459

end page

  • 471

volume

  • 256

international standard serial number (ISSN)

  • 0096-3003

electronic international standard serial number (EISSN)

  • 1873-5649

abstract

  • We obtain a matrix characterization of semiclassical orthogonal polynomials in terms of the Jacobi matrix associated with the multiplication operator in the basis of orthogonal polynomials, and the lower triangular matrix that represents the orthogonal polynomials in terms of the monomial basis of polynomials. We also provide a matrix characterization for coherent pairs of linear functionals.

keywords

  • semiclassical orthogonal polynomials; matrix representation; coherent pairs; jacobi matrices