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# Spectral Transformations of the Laurent Biorthogonal Polynomials, II. Pastro Polynomials

Published:2001-09-01
Printed: Sep 2001
• Luc Vinet
• Alexei Zhedanov
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## Abstract

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
 MSC Classifications: 33D45 - Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)