Results 11 to 20 of about 939,916 (117)
Exceptional đ-Askey-Wilson polynomials and continued fractions [PDF]
Proceedings of the American Mathematical Society, 1991 Two linearly independent solutions of the three-term recurrence relation for the q q -Askey-Wilson polynomials are obtained
Gupta, Dharma P., Masson, David R.
openaire +3 more sources
A Polynomial Blossom for the AskeyâWilson Operator [PDF]
Constructive Approximation, 2018 In this paper the authors introduce a blossoming procedure for polynomials related to the Askey-Wilson operator. This blossom is symmetric, multiaffine, and reduces to the complex representation of the polynomial on a certain diagonal. This Askey-Wilson blossom can be used to find the Askey-Wilson derivative of a polynomial of any order.
Simeonov, Plamen, Goldman, Ron
openaire +4 more sources
A generalization of Mehta-Wang determinant and Askey-Wilson polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Motivated by the Gaussian symplectic ensemble, Mehta and Wang evaluated the $nĂn$ determinant $\det ((a+j-i)Î (b+j+i))$ in 2000. When $a=0$, Ciucu and Krattenthaler computed the associated Pfaffian $\mathrm{Pf}((j-i)Î (b+j+i))$ with an application to the
Victor J. W. Guo +3 more
doaj +3 more sources
The Universal Askey-Wilson Algebra [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension Î of AW, obtained from AW by reinterpreting certain parameters as central elements in ...
Paul Terwilliger
doaj +2 more sources
Orthogonal Polynomials of Askey-Wilson Type
, 2022 26 ...
Ismail, Mourad E. H. +2 more
openaire +3 more sources
On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials.
Tom H. Koornwinder
doaj +2 more sources
Terminating Basic Hypergeometric Representations and Transformations for the Askey-Wilson Polynomials. [PDF]
Symmetry (Basel), 2020 In this survey paper, we exhaustively explore the terminating basic hypergeometric representations of the AskeyâWilson polynomials and the corresponding terminating basic hypergeometric transformations that these polynomials ...
Cohl HS, Costas-Santos RS, Ge L.
europepmc +2 more sources
Discrete Analogues of the Erdélyi Type Integrals for Hypergeometric Functions
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 Gasper followed the fractional calculus proof of an ErdĂ©lyi integral to derive its discrete analogue in the form of a hypergeometric expansion. To give an alternative proof, we derive it by following a procedure analogous to a triple series manipulationâbased proof of the ErdĂ©lyi integral, due to âJoshi and Vyasâ. Motivated from this alternative way of
Yashoverdhan Vyas +5 more
wiley +1 more source
On Another Characterization of Askey-Wilson Polynomials
Results in Mathematics, 2022 In this paper we show that the only sequences of orthogonal polynomials $(P_n)_{n\geq 0}$ satisfying \begin{align*} Ï(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*} ($c_n\neq 0$) where $Ï$ is a well chosen polynomial of degree at most two, $\mathcal{D}_q$ is the Askey-Wilson ...
Mbouna, D., Suzuki, A.
openaire +2 more sources
Remarks on AskeyâWilson polynomials and Meixner polynomials of the second kind [PDF]
The Ramanujan Journal, 2021 The purpose of this note is twofold: firstly to characterize all the sequences of orthogonal polynomials $(P_n)_{n\geq 0}$ such that $$ \frac{\triangle}{{\bf \triangle} x(s-1/2)}P_{n+1}(x(s-1/2))=c_n(\triangle +2\,\mathrm{I})P_n(x(s-1/2)), $$ where $\mathrm{I}$ is the identity operator, $x$ defines a class of lattices with, generally, nonuniform step ...
K. Castillo, D. Mbouna, J. Petronilho
openaire +3 more sources