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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

[1] Al-Salam, W. A. and Ismail, M. E. H., A q-beta integral on the unit circle and some biorthogonal functions. Proc. Amer.Math. Soc. 121 (1994), 553–561.Google Scholar
[2] Gasper, G. and Rahman, M., Basic Hypergeometric Series. Cambridge University Press, Cambridge, 1990.Google Scholar
[3] Hendriksen, E. and van Rossum, H., Orthogonal Laurent polynomials. Indag.Math. (Ser. A) 89 (1986), 17–36.Google Scholar
[4] Pastro, P. I., Orthogonal polynomials and some q-beta integrals of Ramanujan. J. Math. Anal. Appl. 112 (1985), 517–540.Google Scholar
[5] Vinet, L. and Zhedanov, A., Spectral transformations of the Laurent biorthogonal polynomials. I. q-Appel polynomials. J. Comp. Appl. Math., to appear.Google Scholar
[6] Zhedanov, A., The “Classical” Laurent biorthogonal polynomials. J. Comp. Appl. Math. 98 (1998), 121–147.Google Scholar
[7] Zhedanov, A., Rational transformations and orthogonal polynomials. J. Comp. Appl. Math. 85 (1997), 67–86.Google Scholar