A family of symmetric second degree semiclassical forms of class s = 2

A regular form (linear functional) u is called semiclassical, if there exist two nonzero polynomials and such that with monic and deg . 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 BS 2 ( u ) + CS ( u ) +  D = 0. R...

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Bibliographic Details
Published in:Arabian journal of mathematics 2012-09, Vol.1 (3), p.363-375
Main Author: Sghaier, Mabrouk
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Research Article
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Summary:A regular form (linear functional) u is called semiclassical, if there exist two nonzero polynomials and such that with monic and deg . 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 BS 2 ( 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 vanishes at zero. These forms generalize those of class s  = 1.
ISSN:2193-5343
2193-5351
2193-5351
DOI:10.1007/s40065-012-0030-5