Abstract
A regular form (linear functional) u is called semiclassical, if there exist two nonzero polynomials \({\Phi}\) and \({\Psi}\) such that \({( \Phi u )^{\prime} + \Psi u = 0}\) with \({\Phi}\) monic and deg \({\Psi > 0}\). Such a form is said to be of second degree if there are polynomials B, C and D such that its Stieltjes function S(u) satisfies BS2(u) + CS(u) + D = 0. Recently, all the symmetric second degree semiclassical forms of class s ≤ 1 were determined. In this paper, by means of the quadratic decomposition, we determine all the symmetric semiclassical forms of class s = 2, which are also of second degree when \({\Phi}\) vanishes at zero. These forms generalize those of class s = 1.
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Sincere thanks are due to the referees for their valuable comments, useful suggestions and for the references brought to my notice.
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Sghaier, M. A family of symmetric second degree semiclassical forms of class s = 2. Arab. J. Math. 1, 363–375 (2012). https://doi.org/10.1007/s40065-012-0030-5
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DOI: https://doi.org/10.1007/s40065-012-0030-5