Results 41 to 50 of about 45,130 (244)
Expansions in the Askey–Wilson polynomials
Journal of Mathematical Analysis and Applications, 2015 Abstract We give a general expansion formula of functions in the Askey–Wilson polynomials and using Askey–Wilson orthogonality we evaluate several integrals. Moreover we give a general expansion formula of functions in polynomials of Askey–Wilson type, which are not necessarily orthogonal.
Mourad E. H. Ismail +2 more
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Orthogonal Basic Hypergeometric Laurent Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2012 The Askey-Wilson polynomials are orthogonal polynomials in$x = cos heta$, which are given as a terminating $_4phi_3$ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in $z=e^{iheta}$, which are given as a ...
Mourad E.H. Ismail, Dennis Stanton
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General solutions and applications of the coupled Drinfel’d–Sokolov–Wilson equation
Examples and Counterexamples, 2023 We report a new batch of wave solutions for the coupled Drinfel’d–Sokolov–Wilson equation which represents a coupled system of nonlinear partial differential equations (NLPDEs).
Shreya Mitra +2 more
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On Solutions of Holonomic Divided-Difference Equations on Nonuniform Lattices
Axioms, 2013 The main aim of this paper is the development of suitable bases that enable the direct series representation of orthogonal polynomial systems on nonuniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this
Salifou Mboutngam +3 more
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Exact results and Schur expansions in quiver Chern-Simons-matter theories
Journal of High Energy Physics, 2020 We study several quiver Chern-Simons-matter theories on the three-sphere, combining the matrix model formulation with a systematic use of Mordell’s integral, computing partition functions and checking dualities.
Leonardo Santilli, Miguel Tierz
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Perturbative analysis of the colored Alexander polynomial and KP soliton τ-functions
Nuclear Physics B, 2021 In this paper we study the group theoretic structures of colored HOMFLY polynomials in a specific limit. The group structures arise in the perturbative expansion of SU(N) Chern-Simons Wilson loops, while the limit is N→0.
V. Mishnyakov, A. Sleptsov
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Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III [PDF]
, 2016 In a previous paper, we presented conjectures of the recurrence relations with constant coefficients for the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson and Askey-Wilson types.
Odake, Satoru
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Nevanlinna Theory of the Wilson Divided-difference Operator
, 2017 Sitting at the top level of the Askey-scheme, Wilson polynomials are regarded as the most general hypergeometric orthogonal polynomials. Instead of a differential equation, they satisfy a second order Sturm-Liouville type difference equation in terms of ...
Cheng, Kam Hang, Chiang, Yik-Man
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An Eigenvalue Problem for the Associated Askey–Wilson Polynomials [PDF]
, 2020 AmS-LaTeX; 15 ...
Sergei K. Suslov +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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