Results 51 to 60 of about 2,394 (105)
Exceptional Askey–Wilson-type polynomials through Darboux–Crum transformations [PDF]
Journal of Physics A: Mathematical and Theoretical, 2010 An alternative derivation is presented of the infinitely many exceptional Wilson and Askey-Wilson polynomials, which were introduced by the present authors in 2009. Darboux-Crum transformations intertwining the discrete quantum mechanical systems of the original and the exceptional polynomials play an important role.
Odake, Satoru, Sasaki, Ryu
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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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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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, 2005 The equilibrium positions of the multi-particle classical Calogero-Sutherland-Moser (CSM) systems with rational/trigonometric potentials associated with the classical root systems are described by the classical orthogonal polynomials; the Hermite ...
Odake, S., Sasaki, R.
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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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, 2019 Via the solutions of systems of algebraic equations of Bethe Ansatz type, we arrive at bounds for the zeros of orthogonal (basic) hypergeometric polynomials belonging to the Askey-Wilson, Wilson and continuous Hahn families.Comment: 21 pages ...
Emsiz, E., van Diejen, J. F.
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