{
  "id": "1801.03654",
  "version": "v1",
  "published": "2018-01-11T07:58:34.000Z",
  "updated": "2018-01-11T07:58:34.000Z",
  "title": "Proving some identities of Gosper on $q$-trigonometric functions",
  "authors": [
    "Mohamed El Bachraoui"
  ],
  "comment": "Accepted in Proc. Amer. Math. Soc",
  "categories": [
    "math.NT"
  ],
  "abstract": "Gosper introduced the functions $\\sin_q z$ and $\\cos_q z$ as $q$-analogues for the trigonometric functions $\\sin z$ and $\\cos z$ respectively. He stated but did not prove a variety of identities involving these two $q$-trigonometric functions. In this paper, we shall use the theory of elliptic functions to prove three formulas from the list of Gosper on the functions $\\sin_q z$ and $\\cos_q z$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-11T07:58:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33E05",
      "11F11",
      "11F12"
    ],
    "keywords": [
      "trigonometric functions",
      "identities",
      "elliptic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}