On some operational representations of -polynomials
On the limit from -Racah polynomials to big -Jacobi polynomials.
On the symmetries of the -Bernoulli polynomials.
Orthogonal polynomials and recurrence equations, operator equations and factorization.
Orthogonal -polynomials related to perturbed linear form.
-classical orthogonal polynomials: A very classical approach.
-orthogonal polynomials related to the quantum group .
-Selberg integrals and Macdonald polynomials
Quantum algebras and associated with certain -Hahn polynomials: a revisited approach.
Raising and lowering operators for Askey-Wilson polynomials.
Representations of the quantum algebra and discrete -ultraspherical polynomials.
Riesz potentials derived by one-mode interacting Fock space approach
The main aim of this short paper is to study Riesz potentials on one-mode interacting Fock spaces equipped with deformed annihilation, creation, and neutral operators with constants and , as in equations (1.4)-(1.6). First, to emphasize the importance of these constants, we summarize our previous results on the Hilbert space of analytic L² functions with respect to a probability measure on ℂ. Then we consider the Riesz kernels of order 2α, , on ℂ if , which can be derived from the Bessel...
Riordan arrays, Sheffer sequences and “orthogonal” polynomials.
Spherical functions on a family of quantum 3-spheres
The combinatorics of the Al-Salam-Chihara -Charlier polynomials.
The Hahn-Exton q-Bessel function as the characteristic function of a Jacobi matrix
A family T(ν), ν ∈ ℝ, of semiinfinite positive Jacobi matrices is introduced with matrix entries taken from the Hahn-Exton q-difference equation. The corresponding matrix operators defined on the linear hull of the canonical basis in ℓ2(ℤ+) are essentially self-adjoint for |ν| ≥ 1 and have deficiency indices (1, 1) for |ν| < 1. A convenient description of all self-adjoint extensions is obtained and the spectral problem is analyzed in detail. The spectrum is discrete and the characteristic equation...
The relationship between Zhedanov's algebra and the double affine Hecke algebra in the rank one case.
The sharpness of convergence results for -Bernstein polynomials in the case
Due to the fact that in the case the -Bernstein polynomials are no longer positive linear operators on the study of their convergence properties turns out to be essentially more difficult than that for In this paper, new saturation theorems related to the convergence of -Bernstein polynomials in the case are proved.
Topics on Meixner families
We shed some light on the inter-connections between different characterizations leading to the classical Meixner family. This allows us to give free analogs of both Sheffer's and Al-Salam and Chihara's characterizations in the classical case by the use of the free derivative operator. The paper closes with a discussion of the q-deformed case, |q| < 1.
Tridiagonal symmetries of models of nonequilibrium physics.