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

Paweł J. Szabłowski

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

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

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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.

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《Demonstratio Mathematica》 |2013年第4期|679-708|共30页
作者
Paweł J. Szabłowski;
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作者单位

Department of Mathematics and Information Sciences, Warsaw University of Technology;

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正文语种英语
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q-Hermite; Al-Salam–Chihara; Rogers–Szegö; Chebyshev polynomials; q-ultraspherical polynomials; summing kernels; generalization of Poisson–Mehler kernel; generalization of Kibble–Slepian formula;

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

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