Quantum algebra approach to q Gegenbauer polynomials

Gegenbauer Polynomials and Semiseparable Matrices

In this paper, we develop a new O(n logn) algorithm for converting coefficients between expansions in different families of Gegenbauer polynomials up to a finite degree n. To this end, we show that the corresponding linear mapping is represented by the eigenvector matrix of an explicitly known diagonal plus upper triangular semiseparable matrix. The method is based on a new efficient algorithm ...

Information entropy of Gegenbauer polynomials

The information entropy of Gegenbauer polynomials is relevant since this is related to the angular part of the information entropies of certain quantum mechanical systems such as the harmonic oscillator and the hydrogen atom in D dimensions. We give an effective method to compute the entropy for Gegenbauer polynomials with an integer parameter and obtain the first few terms in the asymptotic ex...

MULTIVARIABLE q-HAHN POLYNOMIALS AS COUPLING COEFFICIENTS FOR QUANTUM ALGEBRA REPRESENTATIONS

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. 2000 Mathematics Subject Classification. 17B37, 33D70, 33D80.

q-Deformed Superconformal Algebra on Quantum Superspace

A quantum deformation of 4-dimensional superconformal algebra realized on quantum superspace is investigated. We study the differential calculus and the action of the quantum generators corresponding to slq(1|4) which act on the quantum superspace. We derive deformed su(1|2, 2) algebras from the deformed sl(1|4) algebra. Through a contraction procedure we obtain a deformed super-Poincaré algebr...

An Integral Formula for Generalized Gegenbauer Polynomials and Jacobi Polynomials