Results 11 to 20 of about 3,786,908 (243)
Casoratian identities for the Wilson and Askey-Wilson polynomials [PDF]
Journal of Approximation Theory, 2013 Infinitely many Casoratian identities are derived for the Wilson and Askey-Wilson polynomials in parallel to the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials, which were reported recently by the present authors.
S. Odake, R. Sasaki
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A characterization of Askey-Wilson polynomials [PDF]
Proceedings of the American Mathematical Society, 2017 We show that the only monic orthogonal polynomials $\{P_n\}_{n=0}^{\infty}$ that satisfy $$\pi(x)\mathcal{D}_{q}^2P_{n}(x)=\sum_{j=-2}^{2}a_{n,n+j}P_{n+j}(x),\; x=\cos\theta,\;~ a_{n,n-2}\neq 0,~ n=2,3,\dots,$$ where $\pi(x)$ is a polynomial of degree at
M. K. Nangho, K. Jordaan
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On the Krall-type Askey-Wilson Polynomials [PDF]
Journal of Approximation Theory, 2012 In this paper the general Krall-type Askey-Wilson polynomials are introduced. These polynomials are obtained from the Askey-Wilson polynomials via the addition of two mass points to the weight function of them at the points $\pm1$.
Askey +24 more
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Multi-indexed Wilson and Askey–Wilson polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2012 As the third stage of the project multi-indexed orthogonal polynomials, we present, in the framework of ‘discrete quantum mechanics’ with pure imaginary shifts in one dimension, the multi-indexed Wilson and Askey–Wilson polynomials.
S. Odake, R. Sasaki
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The non-symmetric Wilson polynomials are the Bannai-Ito polynomials [PDF]
Proceedings of the American Mathematical Society, 2015 The one-variable non-symmetric Wilson polynomials are shown to coincide with the Bannai-Ito polynomials. The isomorphism between the corresponding degenerate double affine Hecke algebra of type $(C_1^{\vee}, C_1)$ and the Bannai-Ito algebra is ...
Vincent X. Genest, L. Vinet, A. Zhedanov
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Befriending Askey-Wilson polynomials [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2011 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.
P. Szabłowski
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Nonsymmetric Askey-Wilson polynomials and Q-polynomial distance-regular graphs [PDF]
Journal of Combinatorial Theory, Series A, 2015 In his famous theorem (1982), Douglas Leonard characterized the q-Racah polynomials and their relatives in the Askey scheme from the duality property of Q-polynomial distance-regular graphs.
Jae-Ho Lee
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Bispectral extensions of the Askey–Wilson polynomials [PDF]
Journal of Functional Analysis, 2012 Following the pioneering work of Duistermaat and Grunbaum, we call a family {pn(x)}n=0∞ of polynomials bispectral, if the polynomials are simultaneously eigenfunctions of two commutative algebras of operators: one consisting of difference operators ...
P. Iliev
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Askey--Wilson polynomials, quadratic harnesses and martingales
The Annals of Probability, 2010 We use orthogonality measures of Askey--Wilson polynomials to construct Markov processes with linear regressions and quadratic conditional variances. Askey--Wilson polynomials are orthogonal martingale polynomials for these processes.Comment: Published ...
Bryc, Włodek, Wesołowski, Jacek
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Raising and Lowering Operators for Askey-Wilson Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 In this paper we describe two pairs of raising/lowering operators for Askey-Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the ''classical'' properties
Siddhartha Sahi
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