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Some Functions that Generalize the Askey-Wilson Polynomials
Communications in Mathematical Physics, 1997zbMATH 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, 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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Linear Approximation and Reproduction of Polynomials by Wilson Bases
Journal of Fourier Analysis and Applications, 2002Wilson bases are created multiplying trigonometric functions by translates of a window function with good time/frequency localization. This article investigates the approximation of functions from Sobolev spaces by partial sums of the Wilson basis expansion. In particular, it is shown that the approximation can be improved if polynomials are reproduced.
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Casoratian identities for the Wilson and Askey–Wilson polynomials
Journal of Approximation Theory, 2015Satoru Odake, Ryu Sasaki
exaly
A q-series expansion formula and the Askey–Wilson polynomials
, 2013Zhi-Guo Liu
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On the generalized Askey–Wilson polynomials
Journal of Approximation Theory, 2013R Álvarez-Nodarse
exaly
Some generating functions for the associated Askey-Wilson polynomials
Journal of Computational and Applied Mathematics, 1996Mizan Rahman
exaly