The combinatorics of the Al-Salam-Chihara -Charlier polynomials.
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The Hahn-Exton q-Bessel function as the characteristic function of a Jacobi matrix
F. Štampach, P. Šťovíček (2014)
Special Matrices
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.
Koornwinder, Tom H. (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
The sharpness of convergence results for -Bernstein polynomials in the case
Sofiya Ostrovska (2008)
Czechoslovak Mathematical Journal
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
Marek Bożejko, Nizar Demni (2010)
Banach Center Publications
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.
Aneva, Boyka (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Turán inequalities for symmetric orthogonal polynomials.
Bustoz, Joaquin, Ismail, Mourad E.H. (1997)
International Journal of Mathematics and Mathematical Sciences
Two limit transitions involving multivariable BC type Askey-Wilson polynomials
Jasper Stokman (1997)
Banach Center Publications
In the first part (without proofs) an orthogonality measure with partly discrete and partly continuous support will be introduced for the five parameter family of multivariable BC type Askey-Wilson polynomials. In the second part, the limit transitions from BC type Askey-Wilson polynomials to BC type big and little q-Jacobi polynomials will be described in detail.
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