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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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