{
  "id": "2403.09729",
  "version": "v1",
  "published": "2024-03-13T01:56:22.000Z",
  "updated": "2024-03-13T01:56:22.000Z",
  "title": "Proof and generalization of conjectures of Ramanujan Machine",
  "authors": [
    "Shuma Yamamoto"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "The Ramanujan Machine project predicts new continued fraction representations of numbers expressed by important mathematical constants. Generally, the value of a continued fraction is found by reducing it to a second order linear difference equation. In this paper, we prove 38 conjectures by solving the equation in two ways, use of a differential equation or application of Petkov\\v{s}ek's algorithm. Especially, in the former way, we can get strong generalization of 31 conjectures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-13T01:56:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30B70",
      "39A06"
    ],
    "keywords": [
      "conjectures",
      "second order linear difference equation",
      "generalization",
      "ramanujan machine project predicts",
      "continued fraction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}