A model for the continuous q-ultraspherical polynomials
经典分析与常微分方程
2009-10-28 v1 量子代数
摘要
We provide an algebraic interpretation for two classes of continuous -polynomials. Rogers' continuous -Hermite polynomials and continuous -ultraspherical polynomials are shown to realize, respectively, bases for representation spaces of the -Heisenberg algebra and a -deformation of the Euclidean algebra in these dimensions. A generating function for the continuous -Hermite polynomials and a -analog of the Fourier-Gegenbauer expansion are naturally obtained from these models.
引用
@article{arxiv.math/9504219,
title = {A model for the continuous q-ultraspherical polynomials},
author = {Roberto Floreanini and Luc Vinet},
journal= {arXiv preprint arXiv:math/9504219},
year = {2009}
}