{
  "id": "1401.5368",
  "version": "v3",
  "published": "2014-01-21T16:20:34.000Z",
  "updated": "2014-09-18T14:56:34.000Z",
  "title": "On the equivalence of two fundamental theta identities",
  "authors": [
    "Tom H. Koornwinder"
  ],
  "comment": "v3: 15 pages, minor errors corrected, references added, appendix on four-term theta identities added, accepted by Analysis and Applications",
  "categories": [
    "math.CA",
    "math.QA"
  ],
  "abstract": "Two fundamental theta identities, a three-term identity due to Weierstrass and a five-term identity due to Jacobi, both with products of four theta functions as terms, are shown to be equivalent. One half of the equivalence was already proved by R.J. Chapman in 1996. The history and usage of the two identities, and some generalizations are also discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-25T21:41:32.000Z",
      "abstract": "Two fundamental theta identities, a three-term identity due to Weierstrass and a five-term identity due to Jacobi, both with products of four theta functions as terms, are shown to be equivalent. One half of the equivalence was already proved by R. J. Chapman in 1996. The history and usage of the two identities is also discussed.",
      "comment": "v2: 13 pages, errors corrected and material added",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-09-18T14:56:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33E05",
      "11F27",
      "33-03",
      "01A55"
    ],
    "keywords": [
      "fundamental theta identities",
      "equivalence",
      "three-term identity",
      "five-term identity",
      "theta functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.5368K"
    }
  }
}