A canonical Christoffel transformation of the strict third degree classical linear forms
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Abstract
The aim of this paper is to study several characterizations of a large family of semiclassical linear forms of class one, which are of strict third degree and are not included in either the family of symmetric forms or the quasi-symmetric family. In fact, using the Stieltjes function and the moments, we describe a canonical Christoffel transformation $w$ of the strict third degree classical linear form $\mathcal{V}_{q}^{k, l}:=\mathcal{J}(k+q/3,l-q/3), k+l\geq-1, k, l \in \mathbb{Z}, q\in\{1,2\}$, meaning $w=(x-c)\mathcal{V}_{q}^{k, l}, |c|>1$.
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