Results 51 to 60 of about 2,985,600 (100)

Some generating functions for the associated Askey-Wilson polynomials [PDF]

, 1996
An integral representation is obtained for one family of associated Askey-Wilson polynomials in terms of the ordinary Askey-wilson polynomials.
Rahman, Mizan
core   +1 more source

Connection formulas for Askey--Wilson polynomials and related expansions

We derive and study expansions of and over the Askey--Wilson polynomials. We study these expansions and examine some limits to the continuous dual $q$-Hahn, Al-Salam--Chihara, continuous big $q$-Hermite and continuous $q$-Hermite polynomials and their $q^{-1}$-analogues. The Poisson kernel for the infinite discrete orthogonality relation for the $q^{-1}
Cohl, Howard S., Groenevelt, Wolter
openaire   +2 more sources

Nevanlinna theory of the Askey–Wilson divided difference operator

, 2018
This paper establishes a version of Nevanlinna theory based on Askey–Wilson divided difference operator for meromorphic functions of finite logarithmic order in the complex plane C.
Chiang, Yik Man, Shaoji Feng, Yik-Man Chiang, Feng, Shaoji   +3 more
core   +1 more source

The factorization method for the Askey-Wilson polynomials [PDF]

, 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, Bangerezako, Gaspard   +2 more
core   +1 more source

A Lie algebra related to the universal Askey-Wilson algebra

, 2015
Let $\mathbb{F}$ denote an algebraically closed field. Denote the three-element set by $\mathcal{X}=\{A,B,C\}$, and let $\mathbb{F}\left$ denote the free unital associative $\mathbb{F}$-algebra on $\mathcal{X}$. Fix a nonzero $q\in\mathbb{F}$ such that $q^4\neq 1$. The universal Askey-Wilson algebra $Δ$ is the quotient space $\mathbb{F}\left/\mathbb{I}$
openaire   +3 more sources

Formulas And Identities Involving The Askey-Wilson Operator

, 2016
We derive two new versions of Cooper\u27s formula for the iterated Askey-Wilson operator. Using the second version of Cooper\u27s formula and the Leibniz rule for the iterated Askey-Wilson operator, we derive several formulas involving this operator.
Ismail, Mourad E.H., Simeonov, Plamen
core   +1 more source

On the Askey-Wilson and Rogers Polynomials

, 1988
The q-shifted factorial (a)n or (a; q)n isand an empty product is interpreted as 1. Recently, Askey and Wilson [6] introduced the polynomials1.1where1.2and1.3We shall refer to these polynomials as the Askey-Wilson polynomials or the orthogonal 4ϕ3 ...
Dennis Stanton, Mourad E. H. Ismail
core   +1 more source

A generalization of the Askey-Wilson relations using a projective geometry

Journal of Algebraic Combinatorics
In this paper, we present a generalization of the Askey-Wilson relations that involves a projective geometry. A projective geometry is defined as follows. Let $h>k\geq 1$ denote integers. Let $\mathbb{F}_{q}$ denote a finite field with $q$ elements. Let $\mathcal{V}$ denote an $(h+k)$-dimensional vector space over $\mathbb{F}_{q}$.
openaire   +2 more sources

Nouvelles perspectives sur les algèbres de type Askey–Wilson [PDF]

, 2021
Cette thèse se divise en trois parties qui peuvent être toutes regroupées autour d'une même bannière : l'étude de structures algébriques reliées aux algèbres de type Askey–Wilson.
Gaboriaud, Julien
core  

On the structure and probabilistic interpretation of Askey–Wilson densities and polynomials with complex parameters [PDF]

, 2011
We give equivalent forms of the Askey–Wilson polynomials expressing them with the help of the Al-Salam–Chihara polynomials. After restricting parameters of the Askey–Wilson polynomials to complex conjugate pairs we expand the Askey–Wilson weight function
Paweł J. Szabłowski, Szabłowski, Paweł J.   +1 more
core   +1 more source