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Askey-Wilson Polynomials and Branching Laws

, 2022
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. The Askey-Wilson polynomials are one of the most general 1-variable special functions.
Back, Allen, Oersted, Bent, Sahi, Siddhartha, Speh, Birgit   +3 more
openaire   +3 more sources

Multi-indexed Wilson and Askey–Wilson polynomials [PDF]

Journal of Physics A: Mathematical and Theoretical, 2013
As the third stage of the project multi-indexed orthogonal polynomials, we present, in the framework of 'discrete quantum mechanics' with pure imaginary shifts in one dimension, the multi-indexed Wilson and Askey-Wilson polynomials. They are obtained from the original Wilson and Askey-Wilson polynomials by multiple application of the discrete analogue ...
Odake, Satoru, Sasaki, Ryu
openaire   +2 more sources

Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of quantum classical orthogonal polynomials

Journal of Advanced Research, 2010
Formulae expressing explicitly the q-difference derivatives and the moments of the polynomials Pn(x ; q) ∈ T (T ={Pn(x ; q) ∈ Askey–Wilson polynomials: Al-Salam-Carlitz I, Discrete q-Hermite I, Little (Big) q-Laguerre, Little (Big) q-Jacobi, q-Hahn ...
Eid H. Doha, Hany M. Ahmed
doaj   +1 more source

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

Expansions in the Askey–Wilson polynomials

Journal of Mathematical Analysis and Applications, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ismail, Mourad E.H., Stanton, Dennis
openaire   +3 more sources

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

Degenerate Sklyanin algebras, Askey–Wilson polynomials and Heun operators [PDF]

Journal of Physics A: Mathematical and Theoretical, 2020
Abstract The q-difference equation, the shift and the contiguity relations of the Askey–Wilson polynomials are cast in the framework of the three and four-dimensional degenerate Sklyanin algebras s
Julien Gaboriaud, Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov   +3 more
openaire   +3 more sources

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