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Moments of Askey-Wilson polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 New formulas for the $n^{\mathrm{th}}$ moment $\mu_n(a,b,c,d;q)$ of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and ...
Jang Soo Kim, Dennis Stanton
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On the generalized 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 $\pm1$.
R. Álvarez-Nodarse +1 more
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Askey–Wilson polynomials, quadratic harnesses and martingales [PDF]
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 ...
Włodek Bryc, Jacek Wesołowski
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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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On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials.
Tom H. Koornwinder
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Two-Variable Wilson Polynomials and the Generic Superintegrable System on the 3-Sphere [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators ...
Ernie G. Kalnins +2 more
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Wilson polynomials and the Lorentz transformation properties of the parity operator [PDF]
, 2005 The parity operator for a parity-symmetric quantum field theory transforms as an infinite sum of irreducible representations of the homogeneous Lorentz group.
Carl M. Bender +2 more
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Bispectrality of the Complementary Bannai-Ito Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 A one-parameter family of operators that have the complementary Bannai-Ito (CBI) polynomials as eigenfunctions is obtained. The CBI polynomials are the kernel partners of the Bannai-Ito polynomials and also correspond to a q→−1 limit of the Askey-Wilson ...
Vincent X. Genest +2 more
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A generalization of Mehta-Wang determinant and Askey-Wilson polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Motivated by the Gaussian symplectic ensemble, Mehta and Wang evaluated the $n×n$ determinant $\det ((a+j-i)Γ (b+j+i))$ in 2000. When $a=0$, Ciucu and Krattenthaler computed the associated Pfaffian $\mathrm{Pf}((j-i)Γ (b+j+i))$ with an application to the
Victor J. W. Guo +3 more
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The Universal Askey-Wilson Algebra [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension Δ of AW, obtained from AW by reinterpreting certain parameters as central elements in ...
Paul Terwilliger
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