Results 31 to 40 of about 3,345,023 (270)
On Some Limit Cases of Askey–Wilson Polynomials
Journal of Approximation Theory, 1998 AbstractWe show that limit transitions from Askey–Wilson polynomials toq-Racah, little and bigq-Jacobi polynomials can be made rigorous on the level of their orthogonality measures in a suitable weak sense. This allows us to derive the orthogonality relations and norm evaluations for theq-Racah polynomials, little and bigq-Jacobi polynomials by taking ...
Stokman, J.V., Koornwinder, T.H.
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The factorization method for the Askey–Wilson polynomials
Journal of Computational and Applied Mathematics, 1999 A special Infeld-Hall factorization is given for the Askey-Wilson second order q-difference operator. It is then shown how to deducd a generalization of the corresponding Askey-Wilson polynomials.
Gaspard Bangerezako
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Orthogonal Polynomials of Askey-Wilson Type [PDF]
arXiv, 2022 26 ...
Ismail, Mourad E. H. +2 more
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Nonsymmetric Jacobi and Wilson-type polynomials [PDF]
International Mathematics Research Notices, 2006 Consider a root system of type $BC_1$ on the real line $\mathbb R$ with general positive multiplicities. The Cherednik-Opdam transform defines a unitary operator from an $L^2$-space on $\mathbb R$ to a $L^2$-space of $\mathbb C^2$-valued functions on $\mathbb R^+$ with the Harish-Chandra measure $|c(\lam)|^{-2}d\lam$.
Genkai Zhang, Lizhong Peng
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Terminating Basic Hypergeometric Representations and Transformations for the Askey-Wilson Polynomials. [PDF]
Symmetry (Basel), 2020 In this survey paper, we exhaustively explore the terminating basic hypergeometric representations of the Askey–Wilson polynomials and the corresponding terminating basic hypergeometric transformations that these polynomials satisfy.
Cohl HS, Costas-Santos RS, Ge L.
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A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials [PDF]
, 2012 We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for
Victor J. W. Guo +3 more
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Generalized Bochner theorem: Characterization of the Askey–Wilson polynomials
Journal of Computational and Applied Mathematics, 2008 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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Askey-Wilson Polynomials and Branching Laws
, 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.
Back, Allen +3 more
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Multivariable Wilson polynomials and degenerate Hecke algebras [PDF]
Selecta Mathematica, 2009 We study a rational version of the double affine Hecke algebra associated to the nonreduced affine root system of type $(C^\vee_n,C_n)$. A certain representation in terms of difference-reflection operators naturally leads to the definition of nonsymmetric versions of the multivariable Wilson polynomials.
Wolter Groenevelt
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Liquid-vapor equilibrium and evaporation rate of Cd-Zn liquid alloy [PDF]
Journal of Mining and Metallurgy. Section B: Metallurgy, 2021 In this study, LVE (liquid-vapor equilibrium) data of cadmium-zinc system were determined at a pressure of 7.5 Pa. We compare the use of the Redlich-Kister polynomials with the Wilson equation in fitting activities.
Zhao W.-C., Xu B.-Q., Yang H.-W.
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