Affiliation:
1. University of Monastir, Faculty of Sciences of Monastir, Department of Mathematics, Monastir, Tunisia
2. Departamento de Matemáticas, Universidad Carlos III de Madrid, Leganés, Spain
Abstract
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.
Publisher
National Library of Serbia
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