%0 Journal Article
%T A model for the continuous q-ultraspherical polynomials
%A Roberto Floreanini
%A Luc Vinet
%J Mathematics
%D 1995
%I arXiv
%R 10.1063/1.530998
%X We provide an algebraic interpretation for two classes of continuous $q$-polynomials. Rogers' continuous $q$-Hermite polynomials and continuous $q$-ultraspherical polynomials are shown to realize, respectively, bases for representation spaces of the $q$-Heisenberg algebra and a $q$-deformation of the Euclidean algebra in these dimensions. A generating function for the continuous $q$-Hermite polynomials and a $q$-analog of the Fourier-Gegenbauer expansion are naturally obtained from these models.
%U http://arxiv.org/abs/math/9504219v1