Results 11 to 20 of about 7,854 (155)
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 $$\pi(x)\mathcal{D}_{q}^2P_{n}(x)=\sum_{j=-2}^{2}a_{n,n+j}P_{n+j}(x),\; x=\cos\theta,\;~ a_{n,n-2}\neq 0,~ n=2,3,\dots,$$ where $\pi(x)$ is a polynomial of degree at
Maurice Kenfack Nangho, Kerstin Jordaan
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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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Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials [PDF]
Journal of Mathematical Physics, 2004 We show that the equilibrium positions of the Ruijsenaars-Schneider-van Diejen systems with the trigonometric potential are given by the zeros of the Askey-Wilson polynomials with five parameters.
Askey R. +3 more
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Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials. [PDF]
Proc Natl Acad Sci U S A, 2010 We introduce some combinatorial objects called staircase tableaux, which have cardinality 4nn !, and connect them to both the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials.
Corteel S, Williams LK.
europepmc +3 more sources
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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Degenerate Sklyanin algebras, Askey–Wilson polynomials and Heun operators [PDF]
Journal of Physics A: Mathematical and Theoretical, 2020 The q-difference equation, the shift and the contiguity relations of the Askey–Wilson polynomials are cast in the framework of the three and four-dimensional degenerate Sklyanin algebras ska3 and ska4 .
Julien Gaboriaud +7 more
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Remarks on Askey–Wilson polynomials and Meixner polynomials of the second kind [PDF]
The Ramanujan Journal, 2021 The purpose of this note is to characterize all the sequences of orthogonal polynomials (Pn)n≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
K. Castillo, D. Mbouna, J. Petronilho
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A characterization of the Rogers q-hermite polynomials
International Journal of Mathematics and Mathematical Sciences, 1995 In this paper we characterize the Rogers q-Hermite polynomials as the only orthogonal polynomial set which is also 𝒟q-Appell where 𝒟q is the Askey-Wilson finite difference operator.
Waleed A. Al-Salam
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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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A Quantum Algebra Approach to Multivariate Askey–Wilson Polynomials [PDF]
International Mathematics Research Notices, 2018 We study matrix elements of a change of basis between two different bases of representations of the quantum algebra ${\mathcal{U}}_q(\mathfrak{s}\mathfrak{u}(1,1))$.
Wolter G. M. Groenevelt
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