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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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Two Families of Associated Wilson Polynomials
Canadian Journal of Mathematics, 1990AbstractTwo families of associated Wilson polynomials are introduced. Both families are birth and death process polynomials, satisfying the same recurrence relation but having different initial conditions. Contiguous relations for generalized hypergeometric functions of the type 7F6 are derived and used to find explicit representations for the ...
M. E. H. Ismail +3 more
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On structure formulas for Wilson polynomials
Integral Transforms and Special Functions, 2015By studying various properties of some divided difference operators, we prove that Wilson polynomials are solutions of a second-order difference equation of hypergeometric type. Next, some new structure relations are deduced, the inversion and the connection problems are solved using an algorithmic method.
P. Njionou Sadjang +2 more
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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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Topological materials discovery from crystal symmetry
Nature Reviews Materials, 2021Benjamin J Wieder +2 more
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Associated Askey-Wilson polynomials as Laguerre-Hahn orthogonal polynomials
1988One looks for [formal] orthogonal polynomials satisfying interesting differential or difference relations and equations (Laguerre-Hahn theory). The divided difference operator used here is essentially the Askey-Wilson operator $$Df\left( x \right) = \frac{{E_2 f\left( x \right) - E_1 f\left( x \right)}}{{E_2 x - E_1 x}} = \frac{{f\left( {y_2 \left(
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Copper homeostasis and cuproptosis in health and disease
Signal Transduction and Targeted Therapy, 2022Junxia Min, Fudi Wang
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