Second Degree Linear Forms and Semiclassical Forms of Class One. A Case Study Articles uri icon

publication date

  • January 2022

start page

  • 781

end page

  • 800


  • 3


  • 36

International Standard Serial Number (ISSN)

  • 0354-5180

Electronic International Standard Serial Number (EISSN)

  • 2406-0933


  • Based on their second degree character, in this contribution we study new characterizations of families of symmetric and quasi-symmetric semiclassical linear forms of class one. In fact, by using the Stieltjes function and the moments of those forms, we give necessary and sufficient conditions for a regular form to be at the same time of the second degree, symmetric (resp. quasi-symmetric) and semiclassical of class one. We focus our attention on the link between these forms and the Jacobi forms Tp,q = J(p-1/2, q-1/2), p,q ∈ Z, p+q >= 0. All of them are rational transformations of the first kind Chebychev form T = J (-1/2,-1/2). Finally, we study a family of second degree linear forms which are semiclassical of class one and are not included in the above families


  • Computer Science
  • Mathematics


  • classical and semiclassical forms; orthogonal polynomials; second degree forms; stieltjes function