Results 41 to 50 of about 2,941 (107)
Bivariate Bannai-Ito polynomials
, 2018 A two-variable extension of the Bannai-Ito polynomials is presented. They are obtained via $q\to-1$ limits of the bivariate $q$-Racah and Askey-Wilson orthogonal polynomials introduced by Gasper and Rahman. Their orthogonality relation is obtained. These
Lemay, Jean-Michel, Vinet, Luc
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Nevanlinna Theory of the Wilson Divided-difference Operator
, 2017 Sitting at the top level of the Askey-scheme, Wilson polynomials are regarded as the most general hypergeometric orthogonal polynomials. Instead of a differential equation, they satisfy a second order Sturm-Liouville type difference equation in terms of ...
Cheng, Kam Hang, Chiang, Yik-Man
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Semi-classical Orthogonal Polynomial Systems on Non-uniform Lattices, Deformations of the Askey Table and Analogs of Isomonodromy [PDF]
, 2012 A $\mathbb{D}$-semi-classical weight is one which satisfies a particular linear, first order homogeneous equation in a divided-difference operator $\mathbb{D}$.
Witte, N. S.
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Askey-Wilson Type Functions, With Bound States
, 2003 The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a beautiful ...
A. Kasman +36 more
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Orthogonal Polynomials in Mathematical Physics
, 2017 This is a review of ($q$-)hypergeometric orthogonal polynomials and their relation to representation theory of quantum groups, to matrix models, to integrable theory, and to knot theory.
Chan, Chuan-Tsung +3 more
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A Lie algebra related to the universal Askey-Wilson algebra
, 2015 Let $\mathbb{F}$ denote an algebraically closed field. Denote the three-element set by $\mathcal{X}=\{A,B,C\}$, and let $\mathbb{F}\left$ denote the free unital associative $\mathbb{F}$-algebra on $\mathcal{X}$. Fix a nonzero $q\in\mathbb{F}$ such that $q^4\neq 1$. The universal Askey-Wilson algebra $ $ is the quotient space $\mathbb{F}\left/\mathbb{I}
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A note on the $O_q(\hat{sl_2})$ algebra
, 2010 An explicit homomorphism that relates the elements of the infinite dimensional non-Abelian algebra generating $O_q(\hat{sl_2})$ currents and the standard generators of the $q-$Onsager algebra is proposed.
Baseilhac, P., Belliard, S.
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A family of tridiagonal pairs and related symmetric functions
, 2006 A family of tridiagonal pairs which appear in the context of quantum integrable systems is studied in details. The corresponding eigenvalue sequences, eigenspaces and the block tridiagonal structure of their matrix realizations with respect the dual ...
Askey R +11 more
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A generalization of the Askey-Wilson relations using a projective geometry
In this paper, we present a generalization of the Askey-Wilson relations that involves a projective geometry. A projective geometry is defined as follows. Let $h>k\geq 1$ denote integers. Let $\mathbb{F}_{q}$ denote a finite field with $q$ elements. Let $\mathcal{V}$ denote an $(h+k)$-dimensional vector space over $\mathbb{F}_{q}$.
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On a generalization of the Rogers generating function. [PDF]
J Math Anal Appl, 2019 Cohl HS, Costas-Santos RS, Wakhare TV.
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