Results 51 to 60 of about 2,393 (108)
A Relativistic Conical Function and its Whittaker Limits
Symmetry, Integrability and Geometry: Methods and Applications, 2011 In previous work we introduced and studied a function R(a+,a−,c;v,vˆ) that is a generalization of the hypergeometric function _2F_1 and the Askey-Wilson polynomials.
Simon Ruijsenaars
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Recurrence Relations of the Multi-Indexed Orthogonal Polynomials V : Racah and $q$-Racah types
, 2019 In previous papers, we discussed the recurrence relations of the multi-indexed orthogonal polynomials of the Laguerre, Jacobi, Wilson and Askey-Wilson types. In this paper we explore those of the Racah and $q$-Racah types. For the $M$-indexed ($q$-)Racah
Odake, Satoru
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The structure relation for Askey–Wilson polynomials
Journal of Computational and Applied Mathematics, 2007 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.
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On Some Limit Cases of Askey–Wilson Polynomials
Journal of Approximation Theory, 1998 The authors derive the classical orthogonality relations and norm evaluations for the \(q\)-Racah and \(q\)-Jacobi polynomials by taking limits in the orthogonality relations and norm evaluations for the Askey-Wilson polynomials [\textit{R. Askey} and \textit{J. Wilson}, Mem. Am. Math. Soc. 54, No. 319, 1-55 (1985; Zbl 0572.33012)].
Stokman, J.V., Koornwinder, T.H.
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Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations
Symmetry, Integrability and Geometry: Methods and Applications, 2009 Bethe ansatz formulation is presented for several explicit examples of quasi exactly solvable difference equations of one degree of freedom which are introduced recently by one of the present authors.
Ryu Sasaki, Wen-Li Yang, Yao-Zhong Zhang
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Bispectral extensions of the Askey–Wilson polynomials
Journal of Functional Analysis, 2014 Following the pioneering work of Duistermaat and Gr nbaum, we call a family $\{p_n(x)\}_{n=0}^{\infty}$ of polynomials bispectral, if the polynomials are simultaneously eigenfunctions of two commutative algebras of operators: one consisting of difference operators acting on the degree index $n$, and another one of operators acting on the variable $x$.
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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
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Properties of some families of hypergeometric orthogonal polynomials in several variables
, 1996 Limiting cases are studied of the Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials. We recover recently and not so recently introduced families of hypergeometric orthogonal polynomials in several variables consisting of ...
van Diejen, Jan F.
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An Eigenvalue Problem for the Associated Askey–Wilson Polynomials [PDF]
, 2020 AmS-LaTeX; 15 ...
Bruder, Andrea +2 more
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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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