Probabilistic aspects of Al-Salam–Chihara polynomials
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- by Włodzimierz Bryc, Wojciech Matysiak and Paweł J. Szabłowski PDF
- Proc. Amer. Math. Soc. 133 (2005), 1127-1134 Request permission
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.References
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Additional Information
- Włodzimierz 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
- Paweł J. Szabłowski
- Affiliation: Faculty of Mathematics and Information Science, Warsaw University of Technology, pl. Politechniki 1, 00-661 Warszawa, Poland
- Email: pszablowski@elka.pw.edu.pl
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 1127-1134
- MSC (2000): Primary 33D45; Secondary 05A30, 15A15, 42C05
- DOI: https://doi.org/10.1090/S0002-9939-04-07593-8
- MathSciNet review: 2117214