Results 51 to 60 of about 7,854 (155)

Exceptional 𝑞-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 for the special cases a b c d = q m , m = 1 , 2 , … abcd = {q^m},
Dharma P. Gupta, David R. Masson
openalex   +3 more sources

Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz

Nuclear Physics B, 2019
An operator of Heun-Askey-Wilson type is diagonalized within the framework of the algebraic Bethe ansatz using the theory of Leonard pairs. For different specializations and the generic case, the corresponding eigenstates are constructed in the form of ...
Pascal Baseilhac, Rodrigo A. Pimenta
doaj   +1 more source

Application of Galerkin Method to Kirchhoff Plates Stochastic Bending Problem

International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014
In this paper, the Galerkin method is used to obtain approximate solutions for Kirchhoff plates stochastic bending problem with uncertainty over plates flexural rigidity coefficient. The uncertainty in the rigidity coefficient is represented by means of parameterized stochastic processes. A theorem of Lax‐Milgram type, about existence and uniqueness of
Cláudio Roberto Ávila da Silva Júnior, Milton Kist, Marcelo Borges dos Santos, A. Bairi, T. Y. Kam, W. L. Li   +5 more
wiley   +1 more source

Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme

Advances in Mathematical Physics, Volume 2009, Issue 1, 2009., 2009
In this paper, we apply to (almost) all the “named” polynomials of the Askey scheme, as defined by their standard three‐term recursion relations, the machinery developed in previous papers. For each of these polynomials we identify at least one additional recursion relation involving a shift in some of the parameters they feature, and for several of ...
M. Bruschi, F. Calogero, R. Droghei, M. Lakshmanan   +3 more
wiley   +1 more source

The dynamical U(n) quantum group

International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006
We study the dynamical analogue of the matrix algebra M(n), constructed from a dynamical R‐matrix given by Etingof and Varchenko. A left and a right corepresentation of this algebra, which can be seen as analogues of the exterior algebra representation, are defined and this defines dynamical quantum minor determinants as the matrix elements of these ...
Erik Koelink, Yvette Van Norden
wiley   +1 more source

Multivariable q‐Hahn polynomials as coupling coefficients for quantum algebra representations

International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 6, Page 331-358, 2001., 2001
We study coupling coefficients for a multiple tensor product of highest weight representations of the SU(1, 1) quantum group. These are multivariable generalizations of the q‐Hahn polynomials.
Hjalmar Rosengren
wiley   +1 more source

Correction: Cohl, H.S.; Costas-Santos, R.S.; Ge, L. Terminating Basic Hypergeometric Representations and Transformations for the Askey-Wilson Polynomials Symmetry 2020, 12, 1290

Symmetry, 2020
The authors wish to make the following corrections to their paper [...]
H. Cohl, R. S. Costas-Santos, Linus Ge
semanticscholar   +1 more source

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
doaj   +1 more source

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, Maurice Kenfack-Nangho, Mama Foupouagnigni, Wolfram Koepf   +3 more
doaj   +1 more source

Equivalences of the Multi-Indexed Orthogonal Polynomials [PDF]

, 2013
Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion.
Odake, Satoru
core   +3 more sources