Results 31 to 40 of about 901,840 (78)
On First type characterizations of Askey-Wilson polynomials [PDF]
, 2023 In this chapter we characterize Askey-Wilson polynomials including specific and limiting cases of them by some structure relations of the first type.Comment: arXiv admin note: text overlap with arXiv:2301 ...
Mbouna, D., Suzuki, A.
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Double Affine Hecke Algebras of Rank 1 and the Z_3-Symmetric Askey-Wilson Relations
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We consider the double affine Hecke algebra H=H(k_0,k_1,k_0^v,k_1^v;q) associated with the root system (C_1^v,C_1). We display three elements x, y, z in H that satisfy essentially the Z_3-symmetric Askey-Wilson relations.
Paul Terwilliger, Tatsuro Ito
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Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials [PDF]
, 2015 Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials are presented. They are derived as the eigenfunctions of shape invariant and thus exactly solvable quantum mechanical Hamiltonians.
Sasaki, Ryu, Odake, Satoru
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Orthogonal Polynomials of Askey-Wilson Type
, 2022 We study two families of orthogonal polynomials. The first is a finite family related to the Askey-Wilson polynomials but the orthogonality is on the real line.
Zhou, Keru +2 more
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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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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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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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, 2012 Askey-Wilson polynomial refers to a four-parameter family of q-hypergeometric orthogonal polynomials which contains all families of classical orthogonal polynomials (in the wide sense) as special or limit ...
Koornwinder, T.H. +1 more
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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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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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