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On the Zeros of the Askey–Wilson Polynomials, With Applications to Coding Theory
SIAM Journal on Mathematical Analysis, 1987In 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.
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Askey-Wilson polynomials, kernel polynomials and association schemes
Graphs and Combinatorics, 1993For 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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Fourier - Gauss transforms of the Askey - Wilson polynomials
Journal of Physics A: Mathematical and General, 1997The 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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On a Conjecture Involving Askey–Wilson Polynomials
Integral Transforms and Special FunctionsDieudonne Mbouna, Kenier Castillo
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Asymptotics of the Askey–Wilson and q -Jacobi Polynomials
SIAM Journal on Mathematical Analysis, 1986We 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. We also determine the asymptotic behavior of the q-Racah polynomials.
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On the Askey–Wilson Polynomials and a ?-Beta Integral
Proceedings of the American Mathematical Society, 2021Zhi-Guo Liu
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Some Generating Functions for the Associated Askey-Wilson Polynomials
Journal of Computational and Applied Mathematics, 1996Mizan Rahman
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Little and Big q-Jacobi Polynomials and the Askey–Wilson Algebra
Ramanujan Journal, 2020Luc Vinet +2 more
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