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Multi-indexed Wilson and Askey-Wilson polynomials

Multi-indexed Wilson and Askey-Wilson polynomials
As the third stage of the project multi-indexed orthogonal polynomials, we present, in the framework of 'discrete quantum mechanics' with pure imaginary shifts in one dimension, the multi-indexed Wilson and Askey-Wilson polynomials. They are obtained from the original Wilson and Askey-Wilson polynomials by multiple applications of the discrete analogue
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On the families of polynomials forming a part of the so-called Askey--Wilson scheme and their probabilistic applications [PDF]

, 2020
Paweł J. Szabłowski
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Bispectral commutative difference operators for some multivariable Askey-Wilson polynomials

, 2008
Plamen Iliev
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A Ramanujan-type measure for the Askey-Wilson polynomials

, 1995
Natig M. Atakishiyev
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A generalization of the Mehta-Wang determinant and the Askey-Wilson polynomials (Topics in Combinatorial Representation Theory)

, 2012
雅雄 石川, 裕之 田川
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Askey-Wilson polynomials for root systems of type BC

, 1991
Tom H. Koornwinder
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On the Askey-Wilson polynomials

Constructive Approximation, 1992
Classical orthogonal polynomials of a discrete variable on non-uniform lattices were introduced by \textit{R. Askey} and \textit{J. A. Wilson} [SIAM J. Math. Anal. 10, 1008-1016 (1979; Zbl 0437.33014)], and \textit{J. A. Wilson} [ibid. 11, 690-701 (1980; Zbl 0454.33007)] and their main properties were established on the basis of the theory of ...
Atakishiev, N. M., Suslov, S. K.
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?Hidden symmetry? of Askey-Wilson polynomials

Theoretical and Mathematical Physics, 1991
See the review in Zbl 0744.33009.
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Some Functions that Generalize the Askey-Wilson Polynomials

Communications in Mathematical Physics, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Grünbaum, F. Alberto, Haine, Luc
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Fourier - Gauss transforms of the Askey - Wilson polynomials

Journal of Physics A: Mathematical and General, 1997
The classical Fourier-Gauss transform can be written in the form \[ \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}e^{isr-s^2/r}H_n(\sin\kappa s|q)ds =i^nq^{n^2/4}h_n(\sinh\kappa r|q)e^{-r^2/2}, \] where \(q=\exp(-2\kappa^2)\) and \(h_n(x|q)=i^{-n}H_n(ix|q^{-1})\). Here \(H_n(x|q)\) denotes the continuous \(q\)-Hermite polynomial. In [\textit{M.
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