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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Probabilistic aspects of Al-Salam--Chihara polynomials


Authors: Wlodzimierz Bryc, Wojciech Matysiak and Pawel\ J. Szablowski
Journal: Proc. Amer. Math. Soc. 133 (2005), 1127-1134
MSC (2000): Primary 33D45; Secondary 05A30, 15A15, 42C05
Published electronically: September 16, 2004
MathSciNet review: 2117214
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Abstract: We solve the connection coefficient problem between the Al-Salam--Chihara polynomials and the $q$-Hermite polynomials, and we use the resulting identity to answer a question from probability theory. We also derive the distribution of some Al-Salam--Chihara polynomials, and compute determinants of related Hankel matrices.


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Additional Information

Wlodzimierz Bryc
Affiliation: Department of Mathematics, University of Cincinnati, P.O. Box 210025, Cincinnati, Ohio 45221–0025
Email: Wlodzimierz.Bryc@UC.edu

Wojciech Matysiak
Affiliation: Faculty of Mathematics and Information Science, Warsaw University of Technology, pl. Politechniki 1, 00-661 Warszawa, Poland
Email: wmatysiak@elka.pw.edu.pl

Pawel\ J. Szablowski
Affiliation: Faculty of Mathematics and Information Science, Warsaw University of Technology, pl. Politechniki 1, 00-661 Warszawa, Poland
Email: pszablowski@elka.pw.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07593-8
PII: S 0002-9939(04)07593-8
Keywords: $q$-Hermite polynomials, matrix of moments, orthogonal polynomials, determinants, polynomial regression
Received by editor(s): April 22, 2003
Received by editor(s) in revised form: November 30, 2003
Published electronically: September 16, 2004
Additional Notes: This research was partially supported by NSF grant #INT-0332062.
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2004 American Mathematical Society