Results 31 to 40 of about 2,475 (116)
Symmetry, Integrability and Geometry: Methods and Applications, 2013 We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing.
Ernest G. Kalnins +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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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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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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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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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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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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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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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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Bivariate Bannai-Ito polynomials
, 2018 A two-variable extension of the Bannai-Ito polynomials is presented. They are obtained via $q\to-1$ limits of the bivariate $q$-Racah and Askey-Wilson orthogonal polynomials introduced by Gasper and Rahman. Their orthogonality relation is obtained. These
Lemay, Jean-Michel, Vinet, Luc
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