Geodesic
Second degree linear forms and semiclassical forms of class one. a case study
Filomat, Tome 36 (2022) no. 3, p. 781

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DOI

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
DOI : 10.2298/FIL2203781B
Classification : 33C45, 42C05
Keywords: Orthogonal polynomials, Classical and semiclassical forms, Stieltjes function, Second degree forms 
Imed Ben Salah; Francisco Marcellán; Mohamed Khalfallah. Second degree linear forms and semiclassical forms of class one. a case study. Filomat, Tome 36 (2022) no. 3, p. 781 . doi: 10.2298/FIL2203781B
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     title = {Second degree linear forms and semiclassical forms of class one. a case study},
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     pages = {781 },
     year = {2022},
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     doi = {10.2298/FIL2203781B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2203781B/}
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