Results 61 to 70 of about 939,916 (117)
Hidden Symmetries of Stochastic Models
Symmetry, Integrability and Geometry: Methods and Applications, 2007 In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process.
Boyka Aneva
doaj
Generalized Bochner theorem: Characterization of the Askey–Wilson polynomials
Journal of Computational and Applied Mathematics, 2008 Assume that there is a set of monic polynomials $P_n(z)$ satisfying the second-order difference equation $$ A(s) P_n(z(s+1)) + B(s) P_n(z(s)) + C(s) P_n(z(s-1)) = λ_n P_n(z(s)), n=0,1,2,..., N$$ where $z(s), A(s), B(s), C(s)$ are some functions of the discrete argument $s$ and $N$ may be either finite or infinite.
Vinet, Luc, Zhedanov, Alexei
openaire +3 more sources
A Probablistic Origin for a New Class of Bivariate Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an ...
Michael R. Hoare, Mizan Rahman
doaj +1 more source
Multi-indexed Wilson and Askey-Wilson polynomials
, 2015 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.
Sasaki, Ryu, Odake, Satoru
core
Little and big q-Jacobi polynomials and the Askey–Wilson algebra
, 2019 v2: References added. 15 ppInternational audienceThe little and big q-Jacobi polynomials are shown to arise as basis vectors for representations of the Askey–Wilson algebra.
Baseilhac, Pascal +3 more
core +1 more source
The Combinatorics of q-Hermite polynomials and the Askey—Wilson Integral
European Journal of Combinatorics, 1987 A combinatorial proof of \[ I=\frac{(q)_{\infty}}{2\pi}\int^{\pi}_{0}w(\cos \theta,a,b,c,d| q)d\theta = \frac{(abcd)_{\infty}}{(ab)_{\infty}(ac)_{\infty}(ad)_{\infty}(bc) _{\infty}(bd)_{U}(cd)_{\infty}}, \] where \[ w(\cos \theta,a,b,c,d| q)\quad = \] \[ =\quad \frac{(e^{2i\theta})_{\infty}(e^{- 2i\theta})_{\infty}}{(ae^{i\theta})_{\infty}(ae^{-i\quad \
Mourad E. H. Ismail +2 more
openaire +3 more sources
On the Krall-type Askey-Wilson Polynomials
, 2011 In this paper the general Krall-type Askey-Wilson polynomials are introduced. These polynomials are obtained from the Askey-Wilson polynomials via the addition of two mass points to the weight function of them at the points $\pm1$. Several properties of such new family are considered, in particular the three-term recurrence relation and the ...
Alvarez-Nodarse, R. +1 more
openaire +2 more sources
Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials [PDF]
Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials are presented. They are derived as the eigenfunctions of shape invariant and thus exactly solvable quantum mechanical Hamiltonians.
Sasaki, Ryu, Odake, Satoru
core +1 more source
, 2000 34 pages LaTex file, no figuresWe study the tensor product of principal unitary representations of the quantum Lorentz group, prove a decomposition theorem and compute the associated intertwiners. We show that these intertwiners can be expressed in terms
E. Buffenoir +3 more
core +1 more source
A Quantum Algebra Approach to Multivariate Askey–Wilson Polynomials [PDF]
International Mathematics Research Notices, 2019 AbstractWe study matrix elements of a change of basis between two different bases of representations of the quantum algebra ${\mathcal{U}}_q(\mathfrak{s}\mathfrak{u}(1,1))$. The two bases, which are multivariate versions of Al-Salam–Chihara polynomials, are eigenfunctions of iterated coproducts of twisted primitive elements.
openaire +2 more sources