Results 41 to 50 of about 1,056 (198)
On the generalized Askey–Wilson polynomials
Journal of Approximation Theory, 2013 In this paper a generalization of Askey-Wilson polynomials is 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 ±1. Several properties of such new family are considered, in particular the three-term recurrence relation and the representation as ...
Alvarez-Nodarse, R. +1 more
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On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials
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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A characterization of Askey-Wilson polynomials
Proceedings of the American Mathematical Society, 2019 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 ...
Nangho, Maurice Kenfack +1 more
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Bispectrality of the Complementary Bannai-Ito Polynomials
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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General solutions and applications of the coupled Drinfel’d–Sokolov–Wilson equation
Examples and Counterexamples, 2023 We report a new batch of wave solutions for the coupled Drinfel’d–Sokolov–Wilson equation which represents a coupled system of nonlinear partial differential equations (NLPDEs).
Shreya Mitra +2 more
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Two-Variable Wilson Polynomials and the Generic Superintegrable System on the 3-Sphere
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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Exact results and Schur expansions in quiver Chern-Simons-matter theories
Journal of High Energy Physics, 2020 We study several quiver Chern-Simons-matter theories on the three-sphere, combining the matrix model formulation with a systematic use of Mordell’s integral, computing partition functions and checking dualities.
Leonardo Santilli, Miguel Tierz
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Perturbative analysis of the colored Alexander polynomial and KP soliton τ-functions
Nuclear Physics B, 2021 In this paper we study the group theoretic structures of colored HOMFLY polynomials in a specific limit. The group structures arise in the perturbative expansion of SU(N) Chern-Simons Wilson loops, while the limit is N→0.
V. Mishnyakov, A. Sleptsov
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On Solutions of Holonomic Divided-Difference Equations on Nonuniform Lattices
Axioms, 2013 The main aim of this paper is the development of suitable bases that enable the direct series representation of orthogonal polynomial systems on nonuniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this
Salifou Mboutngam +3 more
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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.
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