{
  "id": "2410.17110",
  "version": "v1",
  "published": "2024-10-22T15:35:16.000Z",
  "updated": "2024-10-22T15:35:16.000Z",
  "title": "Identities for the Rogers-Ramanujan Continued Fraction",
  "authors": [
    "Nayandeep Deka Baruah",
    "Pranjal Talukdar"
  ],
  "comment": "To appear in Journal of the Korean Mathematical Society",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove some new modular identities for the Rogers\\textendash Ramanujan continued fraction. For example, if $R(q)$ denotes the Rogers\\textendash Ramanujan continued fraction, then \\begin{align*}&R(q)R(q^4)=\\dfrac{R(q^5)+R(q^{20})-R(q^5)R(q^{20})}{1+R(q^{5})+R(q^{20})},\\\\ &\\dfrac{1}{R(q^{2})R(q^{3})}+R(q^{2})R(q^{3})= 1+\\dfrac{R(q)}{R(q^{6})}+\\dfrac{R(q^{6})}{R(q)}, \\end{align*}and\\begin{align*}R(q^2)=\\dfrac{R(q)R(q^3)}{R(q^6)}\\cdot\\dfrac{R(q) R^2(q^3) R(q^6)+2 R(q^6) R(q^{12})+ R(q) R(q^3) R^2(q^{12})}{R(q^3) R(q^6)+2 R(q) R^2(q^3) R(q^{12})+ R^2(q^{12})}.\\end{align*} In the process, we also find some new relations for the Rogers-Ramanujan functions by using dissections of theta functions and the quintuple product identity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-22T15:35:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F27",
      "11P84",
      "11A55",
      "33D90"
    ],
    "keywords": [
      "rogers-ramanujan continued fraction",
      "quintuple product identity",
      "rogers-ramanujan functions",
      "modular identities",
      "theta functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}