Results 41 to 50 of about 45,205 (253)
A characterization of the Rogers q-hermite polynomials
International Journal of Mathematics and Mathematical Sciences, 1995 In this paper we characterize the Rogers q-Hermite polynomials as the only orthogonal polynomial set which is also đť’źq-Appell where đť’źq is the Askey-Wilson finite difference operator.
Waleed A. Al-Salam
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Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations [PDF]
, 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.
Andrews G E +19 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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An Eigenvalue Problem for the Associated Askey–Wilson Polynomials [PDF]
, 2020 AmS-LaTeX; 15 ...
Sergei K. Suslov +2 more
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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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Two Families of Associated Wilson Polynomials [PDF]
Canadian Journal of Mathematics, 1990 AbstractTwo families of associated Wilson polynomials are introduced. Both families are birth and death process polynomials, satisfying the same recurrence relation but having different initial conditions. Contiguous relations for generalized hypergeometric functions of the type 7F6 are derived and used to find explicit representations for the ...
Mourad E. H. Ismail +3 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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Nonsymmetric Askey–Wilson polynomials and Q-polynomial distance-regular graphs
Journal of Combinatorial Theory, Series A, 2016 In his famous theorem (1982), Douglas Leonard characterized the $q$-Racah polynomials and their relatives in the Askey scheme from the duality property of $Q$-polynomial distance-regular graphs. In this paper we consider a nonsymmetric (or Laurent) version of the $q$-Racah polynomials in the above situation.
Jae-Ho Lee
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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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