We continue to study the simplest closure conditions for chains of spectral transformations of the Laurent biorthogonal polynomials ($\LBP$). It is shown that the 1-1-periodic $q$-closure condition leads to the $\LBP$ introduced by Pastro. We introduce classes of semi-classical and Laguerre-Hahn $\LBP$ associated to generic closure conditions of the chain of spectral transformations.

Keywords:

Laurent orthogonal polynomials, Pastro polynomials, spectral transformations Laurent orthogonal polynomials, Pastro polynomials, spectral transformations

MSC Classifications:

33D45 show english descriptions Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) 33D45 - Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)

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