Results 61 to 70 of about 2,985,600 (100)

A Ramanujan-type measure for the Askey-Wilson polynomials [PDF]

, 1995
A Ramanujan-type representation for the Askey-Wilson q-beta integral, admitting the transformation q to q(exp -1), is obtained. Orthogonality of the Askey-Wilson polynomials with respect to a measure, entering into this representation, is proved.
Atakishiyev, Natig M.
core  

Expansions in Askey-Wilson polynomials via Bailey transform

, 2017
International audienceWe prove a general expansion formula in Askey-Wilson polynomials using Bailey transform and Bressoud inversion. As applications, we give new proofs and generalizations of some recent results of Ismail-Stanton and Liu.
Zeng, Jiang, Zeya Jia, Jiang Zeng, Jia, Zeya   +3 more
core   +1 more source

Askey-Wilson Polynomials and Branching Laws [PDF]

, 2023
Connection coefficient formulas for special functions describe change of basis matrices under a parameter change, for bases formed by the special functions. Such formulas are related to branching questions in representation theory.
Sahi, Siddhartha, Orsted, Bent, Back, Allen, Speh, Birgit   +3 more
core  

Askey-Wilson type functions with bound states

, 2006
The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a beautiful ...
Luc Haine, Plamen Iliev, Haine, Luc, Iliev, P   +3 more
core   +1 more source

On another characterization of Askey-Wilson polynomials

, 2022
In this paper we show that the only sequences of orthogonal polynomials $(P_n)_{n\geq 0}$ satisfying \begin{align*} \phi(x)\mathcal{D}_q P_{n}(x)=a_n\mathcal{S}_q P_{n+1}(x) +b_n\mathcal{S}_q P_n(x) +c_n\mathcal{S}_q P_{n-1}(x), \end{align*} ($c_n\neq 0$)
Mbouna, D., Suzuki, A.
core  

Askey-Wilson relations and Leonard pairs

Askey-Wilson relations and Leonard pairs
It is known that if $ (A, A^*) $ is a Leonard pair, then the linear transformations $ A $, $ A^* $ satisfy the Askey-Wilson relations $ A^2A^* − \betaAA^*A + A^*A^2 − gamma(AA^* + A^*A) − sigmaA^* = gamma^*A^2 + omegaA + etaI, A^*2A − \betaA^*AA^* + AA^*2 − gamma^*(A^*A + AA^*) − sigma^*A = gammaA^*2 + omegaA^* + eta^*I $, for some scalars $ \beta $, $
openaire   +1 more source

On a generalization of the Rogers generating function. [PDF]

J Math Anal Appl, 2019
Cohl HS, Costas-Santos RS, Wakhare TV.
europepmc   +1 more source

Normalized Leonard pairs and Askey-Wilson relations

Normalized Leonard pairs and Askey-Wilson relations
Let $ V $ denote a vector space with finite positive dimension, and let $ (A, A^*) $ denote a Leonard pair on $ V $. As is known, the linear transformations $ A $, $ A^* $ satisfy the Askey-Wilson relations $ A^2A^* − \betaAA^*A + A^*A^2 − gamma(AA^* + A^*A) − sigmaA^* = gamma^*A^2 + omegaA + etaI, A^2A − \betaA^*AA^* + AA^*2 − gamma^*(A^*A + AA ...
openaire   +1 more source

Two limit transitions involving multivariable Askey-Wilson polynomials [PDF]

, 1996
In the first part (without proofs) an orthogonality measure with partly discrete and partly continuous support will be introduced for the five parameter family of multivariable BC type Askey-Wilson polynomials.
Stokman, J.V., Stokman, Jasper
core  

Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials. [PDF]

Proc Natl Acad Sci U S A, 2010
Corteel S, Williams LK.
europepmc   +1 more source