Probabilistic aspects of Al-Salam–Chihara polynomials

Bryc, Włodzimierz; Matysiak, Wojciech; Szabłowski, Paweł

doi:10.1090/S0002-9939-04-07593-8

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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