Results 41 to 50 of about 3,132,788 (112)
Spectral Analysis of Certain Schrödinger Operators
Symmetry, Integrability and Geometry: Methods and Applications, 2012 The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators.
Mourad E.H. Ismail, Erik Koelink
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Nonsymmetric Askey–Wilson polynomials as vector-valued polynomials [PDF]
, 2011 Nonsymmetric Askey-Wilson polynomials are usually written as Laurent polynomials. We write them equivalently as 2-vector-valued symmetric Laurent polynomials.
Tom H. Koornwinder +3 more
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On the Askey-Wilson and Rogers Polynomials
, 1988 The q-shifted factorial (a)n or (a; q)n isand an empty product is interpreted as 1. Recently, Askey and Wilson [6] introduced the polynomials1.1where1.2and1.3We shall refer to these polynomials as the Askey-Wilson polynomials or the orthogonal 4ϕ3 ...
Dennis Stanton, Mourad E. H. Ismail
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Bilateral discrete and continuous orthogonality relations in the $q^{-1}$-symmetric Askey scheme [PDF]
In the $q^{-1}$-symmetric Askey scheme, namely the $q^{-1}$-Askey--Wilson, continuous dual $q^{-1}$-Hahn, $q^{-1}$-Al-Salam--Chihara, continuous big $q^{-1}$-Hermite and continuous $q^{-1}$-Hermite polynomials, we compute bilateral discrete and ...
Cohl, Howard S., Volkmer, Hans
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Multi-indexed Wilson and Askey-Wilson Polynomials [PDF]
, 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.
Ryu Sasaki +3 more
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Hidden Symmetries of Stochastic Models
Symmetry, Integrability and Geometry: Methods and Applications, 2007 In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process.
Boyka Aneva
doaj
Another Type of Forward and Backward Shift Relations for Orthogonal Polynomials in the Askey Scheme [PDF]
The forward and backward shift relations are basic properties of the (basic) hypergeometric orthogonal polynomials in the Askey scheme (Jacobi, Askey-Wilson, $q$-Racah, big $q$-Jacobi etc.) and they are related to the factorization of the differential or
Odake, Satoru
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Connection formulas for Askey--Wilson polynomials and related expansions
We derive and study expansions of and over the Askey--Wilson polynomials. We study these expansions and examine some limits to the continuous dual $q$-Hahn, Al-Salam--Chihara, continuous big $q$-Hermite and continuous $q$-Hermite polynomials and their $q^{-1}$-analogues. The Poisson kernel for the infinite discrete orthogonality relation for the $q^{-1}
Cohl, Howard S., Groenevelt, Wolter
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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 $Δ$ is the quotient space $\mathbb{F}\left/\mathbb{I}$
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Askey-Wilson Polynomials and Branching Laws [PDF]
, 2023 Connection coefficient formulas for special functions describe change of basis matrices under a parameter change, for bases formed by the special functions. Such formulas are related to branching questions in representation theory.
Sahi, Siddhartha +3 more
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