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Probabilistic aspects of Al-Salam--Chihara polynomials

Author(s): Wlodzimierz Bryc; Wojciech Matysiak; Pawel\ J. Szablowski
Journal: Proc. Amer. Math. Soc. 133 (2005), 1127-1134.
MSC (2000): Primary 33D45; Secondary 05A30, 15A15, 42C05
Posted: September 16, 2004
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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: 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
Posted: September 16, 2004
Additional Notes: This research was partially supported by NSF grant \#INT-0332062.
Communicated by: Carmen C. Chicone
Copyright of article: Copyright 2004, American Mathematical Society

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