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

Published online by Cambridge University Press:  20 November 2018

Luc Vinet  and
Alexei Zhedanov
Luc Vinet
Affiliation:
Centre de recherches mathématiques Université de Montréal C.P. 6128, succ. Centre-Ville Montréal, QC H3C 3J7
Alexei Zhedanov
Affiliation:
Donetsk Institute for Physics and Technology Donetsk 83114 Ukraine
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Abstract

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

Keywords

33D45Laurent orthogonal polynomialsPastro polynomialsspectral transformations
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 3 , 01 September 2001 , pp. 337 - 345
Copyright
Copyright © Canadian Mathematical Society 2001

References

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