Elementary observations on Rogers-Szegö polynomials

Abstract

The Rogers-Szegö 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-Szegö polynomials which have nice expansions and Hankel determinants. The Exposition of the paper is elementary and almost self-contained.

Enlarged and updated Version

References in corpus (4)

• A simple approach to some Hankel determinants
• A simple approach to q-Chebyshev polynomials
• Finite q-identities related to well-known theorems of Euler and Gauss
• On a conjecture of Cigler