Results 51 to 60 of about 939,916 (117)
On the Askey--Wilson type integrals [PDF]
, 2023 The Askey--Wilson integral is very important in the theory of orthogonal polynomials. Liu's integral is a generalization of the Askey--Wilson integral with many parameters. With the help of the series rearrangement method, we give the elementary proof of
Wei, Chuanan
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Symmetry, Integrability and Geometry: Methods and Applications, 2007 Zhedanov's algebra AW(3) is considered with explicit structure constants such that, in the basic representation, the first generator becomes the second order q-difference operator for the Askey-Wilson polynomials. It is proved that this representation is
Tom H. Koornwinder
doaj
Two limit transitions involving multivariable Askey-Wilson polynomials [PDF]
, 1996 In the first part (without proofs) an orthogonality measure with partly discrete and partly continuous support will be introduced for the five parameter family of multivariable BC type Askey-Wilson polynomials.
Stokman, Jasper, Stokman, J.V.; id_orcid
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Symmetry, Integrability and Geometry: Methods and Applications, 2008 This paper builds on the previous paper by the author, where a relationship between Zhedanov's algebra AW(3) and the double affine Hecke algebra (DAHA) corresponding to the Askey-Wilson polynomials was established.
Tom H. Koornwinder
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A Ramanujan-type measure for the Askey-Wilson polynomials [PDF]
, 1995 A Ramanujan-type representation for the Askey-Wilson q-beta integral, admitting the transformation q to q(exp -1), is obtained. Orthogonality of the Askey-Wilson polynomials with respect to a measure, entering into this representation, is proved.
Atakishiyev, Natig M.
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Nonnegative Linearization and Quadratic Transformation of Askey-Wilson Polynomials
, 1996 Nonnegative product linearization of the Askey-Wilson polynomials is shown for a wide range of parameters. As a corollary we obtain Rahman's result on the continuous q-Jacobi polynomials with α ≥ β > — 1 and α + β + 1 ≥ 0.
Ryszard Szwarc
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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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Tridiagonal Symmetries of Models of Nonequilibrium Physics
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We study the boundary symmetries of models of nonequilibrium physics where the steady state behaviour strongly depends on the boundary rates. Within the matrix product state approach to many-body systems the physics is described in terms of matrices ...
Boyka Aneva
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The Askey–Wilson polynomials and q-Sturm–Liouville problems [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 1996 AbstractWe find the adjoint of the Askey–Wilson divided difference operator with respect to the inner product on L2(–1, 1, (1– x2)½dx) defined as a Cauchy principal value and show that the Askey-Wilson polynomials are solutions of a q-Sturm–Liouville problem.
Brown, B. Malcolm +2 more
openaire +3 more sources
Lecture hall graphs and the Askey scheme [PDF]
, 2023 We establish, for every family of orthogonal polynomials in the $q$-Askey scheme and the Askey scheme, a combinatorial model for mixed moments and coefficients in terms of paths on the lecture hall graph.
Corteel, Sylvie +3 more
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