Probabilistic aspects of Al-Salam-Chihara polynomials

2003/04/30 by Wlodzimierz Bryc, Wojciech Matysiak, Pawel J. Szablowski
Mathematics · #math.CA #msc:33D45 #msc:05A30 #msc:15A15 #msc:42C05

paper · pdf

published as Proc. Amer. Math. Soc. 133 (2005) 1127-1134 · LaTeX, 8 pages

arxiv created 2003/12/02 · arxiv updated 2009/11/30

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.

Related

• Combinatorial formulas for the coefficients of the Al-Salam-Chihara polynomials
• The Combinatorics of Al-Salam-Chihara q-Laguerre polynomials
• The combinatorics of q-Charlier polynomials
• A counterexample to a conjecture of M. Ismail
• A probabilistic approach to q-polynomial coefficients, Euler and Stirling numbers