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Expansions in the Askey{Wilson Polynomials

Journal of Mathematical Analysis and Applications, 2015
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M. Ismail, D. Stanton
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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 ...
N. Atakishiyev, S. Suslov
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On the zeros of the Askey-Wilson polynomials, with applications to coding theory

SIAM Journal on Mathematical Analysis, 1987
In a symmetric association scheme that is (P and Q)-polynomial, the P and Q eigenmatrices are given by balanced \({}_ 4\Phi_ 3\) Askey-Wilson polynomials. In this paper, the parameters of the Askey-Wilson polynomial are classified so that its zeros are not contained in its spectrum. These results, together with theorems of Biggs and Delsarte, imply the
Laura M. Chihara
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Some Functions that Generalize the Askey–Wilson Polynomials

Communications in Mathematical Physics, 1997
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F. Grünbaum, L. Haine
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A q-series expansion formula and the Askey–Wilson polynomials

The Ramanujan Journal, 2013
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Zhi-Guo Liu
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Askey-Wilson polynomials and the quantum SU(2) group: Survey and applications

Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, 1994
Generalised matrix elements of the irreducible representations of the quantum SU(2) group are defined using certain orthonormal bases of the representation space.
E. Koelink
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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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Asymptotics of the Askey–Wilson and q-Jacobi Polynomials

SIAM Journal on Mathematical Analysis, 1986
Summary: We derive explicit representations and complete asymptotic expansions for the Askey-Wilson \({}_ 4\phi_ 3\) polynomials and the little and big q- Jacobi polynomials. We also give an alternate proof of a Dirichlet-Mehler type formula for the continuous q-ultraspherical polynomials.
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Askey-Wilson polynomials, kernel polynomials and association schemes

Graphs and Combinatorics, 1993
For many of the classical association schemes, there are specific sets of orthogonal polynomials associated with them. When these can be found explicitly, the polynomials can be given as hypergeometric or basic hypergeometric series. A new association scheme was constructed by \textit{A. A. Ivanov}, \textit{M. E. Muzichuk} and \textit{V. A. Ustimenko} [
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Askey-Wilson polynomials as zonal spherical functions on the SU (2) quantum group

, 1993
T. Koornwinder
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