Results 91 to 100 of about 3,132,788 (112)

Expansions in the Askey–Wilson Polynomials

Journal of Mathematical Analysis and Applications, 2015
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 ...
Mourad Ismail, Dennis Stanton
exaly   +3 more sources

On the Generalized Askey–Wilson Polynomials [PDF]

Journal of Approximation Theory, 2013
In this paper a generalization of Askey-Wilson polynomials is introduced. These polynomials are obtained from the Askey-Wilson polynomials via the addition of two mass points to the weight function of them at the points ±1.
Renato Álvarez-Nodarse
exaly   +2 more sources

The Factorization Method for the Askey–Wilson Polynomials

Journal of Computational and Applied Mathematics, 1999
A special Infeld-Hull factorization is given for the Askey-Wilson second order q-difference operator. It is then shown how to deduce a generalization of the corresponding Askey-Wilson polynomials. (C) 1999 Elsevier Science B.V.
Bangerezako, G, Gaspard Bangerezako
exaly   +2 more sources

Casoratian Identities for the Wilson and Askey–Wilson Polynomials

Journal of Approximation Theory, 2015
Infinitely many Casoratian identities are derived for the Wilson and Askey–Wilson polynomials in parallel to the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials, which were reported recently by the present authors.
Satoru Odake, Ryu Sasaki
exaly   +1 more source

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The Addition Formula for Continuous q -Legendre Polynomials and Associated Spherical Elements on the $SU(2)$ Quantum Group Related to Askey–Wilson Polynomials

SIAM Journal on Mathematical Analysis, 1994
The known interpretation of a two-parameter family of Askey–Wilson polynomials as spherical elements on the $SU(2)$ quantum group is extended to an interpretation of a three-parameter (one discrete parameter) family of Askey–Wilson polynomials as associated spherical elements on the $SU(2)$ quantum group.
openaire   +2 more sources

Double Affine Hecke Algebras of Rank 1 and the Z???-Symmetric Askey-Wilson Relations

2019
We consider the double affine Hecke algebra H=H(k???,k???,k???v,k???v;q) associated with the root system (C???v,C???). We display three elements x, y, z in H that satisfy essentially the Z???-symmetric Askey-Wilson relations. We obtain the relations as follows. We work with an algebra ??
Ito, T., Terwilliger, P.
openaire   +1 more source

Q-Fractional Askey–Wilson Integrals and Related Semigroups of Operators

Physica D: Nonlinear Phenomena, 2022
Mourad Ismail, Keru Zhou
exaly  

On the Askey–Wilson Polynomials and a ?-Beta Integral

Proceedings of the American Mathematical Society, 2021
Zhi-Guo Liu
exaly