Elementary observations on Rogers-Szeg\"o polynomials
Classical Analysis and ODEs
2016-03-31 v2 Combinatorics
Abstract
The Rogers-Szeg\"o polynomials are natural q-analogues of Newton binomials. In general they have no closed expression. We consider some exceptional cases which are products of a factor with a closed formula and another one with nice values for q=1 and q=-1. These are related to normalized Rogers-Szeg\"o polynomials which have nice expansions and Hankel determinants. The Exposition of the paper is elementary and almost self-contained.
Cite
@article{arxiv.1602.07850,
title = {Elementary observations on Rogers-Szeg\"o polynomials},
author = {Johann Cigler},
journal= {arXiv preprint arXiv:1602.07850},
year = {2016}
}
Comments
Enlarged and updated Version