Results 31 to 40 of about 7,854 (155)
Symmetry techniques for $q$-series: Askey-Wilson polynomials [PDF]
, 1989 E. G. Kalnins, Willard Miller
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Generalized Bochner theorem: characterization of the Askey-Wilson polynomials [PDF]
Journal of Computational and Applied Mathematics, 2007 Assume that there is a set of monic polynomials $P_n(z)$ satisfying the second-order difference equation $$ A(s) P_n(z(s+1)) + B(s) P_n(z(s)) + C(s) P_n(z(s-1)) = _n P_n(z(s)), n=0,1,2,..., N$$ where $z(s), A(s), B(s), C(s)$ are some functions of the discrete argument $s$ and $N$ may be either finite or infinite. The irreducibility condition $A(s-1)C(
Luc Vinet, Alexei Zhedanov
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The associated Askey-Wilson polynomials [PDF]
Transactions of the American Mathematical Society, 1991 The most general system of basic hypergeometric orthogonal polynomials are the Askey-Wilson polynomials, which are given as a basic hypergeometric series \(_ 4\Phi_ 3\). Like all orthogonal polynomials they satisfy a three-term recurrence relation \[ 2xp_ n(x)=A_ np_{n+1}(x)+B_ np_ n(x)+C_ np_{n-1}(x). \] The recurrence coefficients \(A_ n\), \(B_ n\),
Mourad E. H. Ismail, Mizan Rahman
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Bootstrapping and Askey–Wilson polynomials [PDF]
Journal of Mathematical Analysis and Applications, 2014 The mixed moments for the Askey-Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey-Wilson generating function. An important special case of this hierarchy is a polynomial which satisfies a four term recurrence, and its combinatorics is studied.
Jang Soo Kim, Dennis Stanton
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Askey-Wilson Polynomials and Branching Laws [PDF]
, 2022 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. The Askey-Wilson polynomials are one of the most general 1-variable special functions.
Allen Back +3 more
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The structure relation for Askey–Wilson polynomials [PDF]
Journal of Computational and Applied Mathematics, 2006 An explicit structure relation for Askey-Wilson polynomials is given. This involves a divided q-difference operator which is skew symmetric with respect to the Askey-Wilson inner product and which sends polynomials of degree n to polynomials of degree n+1.
Tom H. Koornwinder
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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.
Tom H. Koornwinder
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Selberg integrals, Askey–Wilson polynomials and lozenge tilings of a hexagon with a triangular hole [PDF]
Journal of Combinatorial Theory, 2015 Hjalmar Rosengren
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Tensor product of principal unitary representations of quantum Lorentz group and Askey–Wilson polynomials [PDF]
, 2000 E. Buffenoir, Ph. Roche
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Askey-Wilson polynomials for root systems of type BC
, 1991 Tom H. Koornwinder
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