More on the q-oscillator algebra and q-orthogonal polynomials
Classical Analysis and ODEs
2016-09-06 v1 Quantum Algebra
Abstract
Properties of certain -orthogonal polynomials are connected to the -oscillator algebra. The Wall and -Laguerre polynomials are shown to arise as matrix elements of -exponentials of the generators in a representation of this algebra. A realization is presented where the continuous -Hermite polynomials form a basis of the representation space. Various identities are interpreted within this model. In particular, the connection formula between the continuous big -Hermite polynomials and the continuous -Hermite polynomials is thus obtained, and two generating functions for these last polynomials are algebraically derived.
Cite
@article{arxiv.math/9504218,
title = {More on the q-oscillator algebra and q-orthogonal polynomials},
author = {Roberto Floreanini and Jean LeTourneux and Luc Vinet},
journal= {arXiv preprint arXiv:math/9504218},
year = {2016}
}