{
  "id": "1602.07850",
  "version": "v1",
  "published": "2016-02-25T09:00:27.000Z",
  "updated": "2016-02-25T09:00:27.000Z",
  "title": "Elementary observations on Rogers-Szegö polynomials",
  "authors": [
    "Johann Cigler"
  ],
  "comment": "28 pages",
  "categories": [
    "math.CA",
    "math.CO"
  ],
  "abstract": "The Rogers-Szeg\\\"o polynomials are natural q-analogues of Newton binomials. In general there is no closed expression for them. We study some exceptional cases which can be factored into a product of a nice factor with a closed formula and an ugly factor with nice values for q=1 and q=-1. These can be interpreted as extensions of Gauss identity for alternating sums of q-binomial coefficients. In the course of this investigation we were led to many interesting conjectures. The most notable ones are explicit formulae for Hankel determinants of normalized Rogers-Szeg\\\"o polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-25T09:00:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A30",
      "11B65",
      "33D45"
    ],
    "keywords": [
      "elementary observations",
      "polynomials",
      "hankel determinants",
      "natural q-analogues",
      "explicit formulae"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160207850C"
    }
  }
}