Results 11 to 20 of about 45,941 (258)
Nonsymmetric Askey–Wilson polynomials as vector-valued polynomials [PDF]
Applicable Analysis, 2010 Nonsymmetric Askey-Wilson polynomials are usually written as Laurent polynomials. We write them equivalently as 2-vector-valued symmetric Laurent polynomials.
Tom H. Koornwinder, Fethi Bouzeffour
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Befriending Askey–Wilson polynomials [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2014 We recall five families of polynomials constituting a part of the so-called Askey–Wilson scheme. We do this to expose properties of the Askey–Wilson (AW) polynomials that constitute the last, most complicated element of this scheme. In doing so we express AW density as a product of the density that makes q-Hermite polynomials orthogonal times a ...
Paweł J. Szabłowski
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Multiple Wilson and Jacobi-Pineiro polynomials [PDF]
Journal of Approximation Theory, 2003 22 pages, 2 ...
Bernhard Beckermann +2 more
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Turán Inequalities for Symmetric Askey-Wilson Polynomials [PDF]
Rocky Mountain Journal of Mathematics, 2000 The authors study a renormalized \(A-W\) polynomial \(V_n(x)\). Using the Szász technique they establish the inequalities \[ 0\leq V_n^2(x)-V_{n+1} (x)V_{n-1} (x)\leq K, \] where \(K\) is independent of \(x\). The two inequalities hold under certain conditions upon parameters and variable.
Luís Daniel Abreu, J. Bustoz
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Scholarpedia, 2012 Askey-Wilson polynomial refers to a four-parameter family of q-hypergeometric orthogonal polynomials which contains all families of classical orthogonal polynomials (in the wide sense) as special or limit cases.
Tom H. Koornwinder
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The associated Askey-Wilson polynomials [PDF]
Transactions of the American Mathematical Society, 1991 The most general system of basic hypergeometric orthogonal polynomials are the Askey-Wilson polynomials, which are given as a basic hypergeometric series \(_ 4\Phi_ 3\). Like all orthogonal polynomials they satisfy a three-term recurrence relation \[ 2xp_ n(x)=A_ np_{n+1}(x)+B_ np_ n(x)+C_ np_{n-1}(x). \] The recurrence coefficients \(A_ n\), \(B_ n\),
Mourad E. H. Ismail, Mizan Rahman
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Bootstrapping and Askey–Wilson polynomials [PDF]
Journal of Mathematical Analysis and Applications, 2014 The mixed moments for the Askey-Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey-Wilson generating function. An important special case of this hierarchy is a polynomial which satisfies a four term recurrence, and its combinatorics is studied.
Jang Soo Kim, Dennis Stanton
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On another characterization of Askey-Wilson polynomials [PDF]
Results in Mathematics, 2022 In this paper we show that the only sequences of orthogonal polynomials $(P_n)_{n\geq 0}$ satisfying \begin{align*} ϕ(x)\mathcal{D}_q P_{n}(x)=a_n\mathcal{S}_q P_{n+1}(x) +b_n\mathcal{S}_q P_n(x) +c_n\mathcal{S}_q P_{n-1}(x), \end{align*} ($c_n\neq 0$) where $ϕ$ is a well chosen polynomial of degree at most two, $\mathcal{D}_q$ is the Askey-Wilson ...
D. Mbouna, A. Suzuki
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Liquid-vapor equilibrium and evaporation rate of Cd-Zn liquid alloy [PDF]
Journal of Mining and Metallurgy. Section B: Metallurgy, 2021 In this study, LVE (liquid-vapor equilibrium) data of cadmium-zinc system were determined at a pressure of 7.5 Pa. We compare the use of the Redlich-Kister polynomials with the Wilson equation in fitting activities.
Zhao W.-C., Xu B.-Q., Yang H.-W.
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A characterization of Askey-Wilson polynomials [PDF]
Proceedings of the American Mathematical Society, 2018 We show that the only monic orthogonal polynomials $\{P_n\}_{n=0}^{\infty}$ that satisfy $$ (x)\mathcal{D}_{q}^2P_{n}(x)=\sum_{j=-2}^{2}a_{n,n+j}P_{n+j}(x),\; x=\cos ,\;~ a_{n,n-2}\neq 0,~ n=2,3,\dots,$$ where $ (x)$ is a polynomial of degree at most $4$ and $\mathcal{D}_{q}$ is the Askey-Wilson operator, are Askey-Wilson polynomials and their ...
Maurice Kenfack Nangho, Kerstin Jordaan
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