Results 31 to 40 of about 45,130 (244)

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.
Allen Back, Bent Ørsted, Siddhartha Sahi, Birgit Speh   +3 more
openalex   +4 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

The non-symmetric Wilson polynomials are the Bannai–Ito polynomials [PDF]

Proceedings of the American Mathematical Society, 2016
The one-variable non-symmetric Wilson polynomials are shown to coincide with the Bannai-Ito polynomials. The isomorphism between the corresponding degenerate double affine Hecke algebra of type $(C_1^{\vee}, C_1)$ and the Bannai-Ito algebra is established.
Luc Vinet, Vincent X. Genest, Alexei Zhedanov   +2 more
openaire   +3 more sources

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

The colored Jones polynomials as vortex partition functions

Journal of High Energy Physics, 2021
We construct 3D N $$ \mathcal{N} $$ = 2 abelian gauge theories on S $$ \mathbbm{S} $$ 2 × S $$ \mathbbm{S} $$ 1 labeled by knot diagrams whose K-theoretic vortex partition functions, each of which is a building block of twisted indices, give the colored ...
Masahide Manabe, Seiji Terashima, Yuji Terashima   +2 more
doaj   +1 more source

Bootstrapping and Askey–Wilson polynomials

Journal of Mathematical Analysis and Applications, 2015
The mixed moments for the Askey-Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey-Wilson generating function. An important special case of this hierarchy is a polynomial which satisfies a four term recurrence, and its combinatorics is studied.
Jang Soo Kim, Dennis Stanton
openaire   +3 more sources

Bispectrality of Multivariable Racah–Wilson Polynomials [PDF]

Constructive Approximation, 2009
minor ...
Plamen Iliev, Jeffrey S. Geronimo
openaire   +4 more sources

Non-symmetric Jacobi and Wilson type polynomials [PDF]

International Mathematics Research Notices, 2005
Consider a root system of type $BC_1$ on the real line $\mathbb R$ with general positive multiplicities. The Cherednik-Opdam transform defines a unitary operator from an $L^2$-space on $\mathbb R$ to a $L^2$-space of $\mathbb C^2$-valued functions on $\mathbb R^+$ with the Harish-Chandra measure $|c(\lam)|^{-2}d\lam$.
Lizhong Peng, Genkai Zhang
openalex   +5 more sources

A characterization of the Rogers q-hermite polynomials

International Journal of Mathematics and Mathematical Sciences, 1995
In this paper we characterize the Rogers q-Hermite polynomials as the only orthogonal polynomial set which is also 𝒟q-Appell where 𝒟q is the Askey-Wilson finite difference operator.
Waleed A. Al-Salam
doaj   +1 more source

Chern-Simons perturbative series revisited

Physics Letters B, 2021
A group-theoretical structure in a perturbative expansion of the Wilson loops in the 3d Chern-Simons theory with SU(N) gauge group is studied in symmetric approach.
E. Lanina, A. Sleptsov, N. Tselousov
doaj   +1 more source