On the q-Hermite polynomials and their relationship with some other families of orthogonal polynomials

• Autorzy: Szabłowski P. J.
• Języki publikacji: EN

Abstrakty

EN

We review properties of the q-Hermite polynomials and indicate their links with the Chebyshev, Rogers–Szegö, Al-Salam–Chihara, continuous q-utraspherical polynomials. In particular, we recall the connection coefficients between these families of polynomials. We also present some useful and important finite and infinite expansions involving polynomials of these families including symmetric and non-symmetric kernels. In the paper, we collect scattered throughout literature useful but not widely known facts concerning these polynomials. It is based on 43 positions of predominantly recent literature.

Słowa kluczowe

EN

Hermite polynomials; Al-Salam–Chihara polynomials; Rogers–Szegö polynomials; Chebyshev polynomials; q-ultraspherical polynomials; summing kernels; Poisson-Mehler kernel; Kibble-Slepian formula

PL

wielomiany Hermite'a; wielomiany Al-Salam–Chihara; wielomiany Rogers–Szegö; wielomiany Czebyszewa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2013
• Tom: Vol. 46, nr 4
• Strony: 679--708
• Opis fizyczny: Bibliogr. 43 poz.

Twórcy

autor

Szabłowski P. J.

• Department of Mathematics and Information Sciences, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland

Bibliografia

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