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arXiv · 1602.07850

Elementary observations on Rogers-Szeg\"o polynomials

Johann Cigler
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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.

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Johann Cigler. 2016-02-25. Elementary observations on Rogers-Szeg\"o polynomials. https://arxiv.org/abs/1602.07850

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