{
  "id": "2307.14639",
  "version": "v1",
  "published": "2023-07-27T06:15:34.000Z",
  "updated": "2023-07-27T06:15:34.000Z",
  "title": "Explicit error bound of the elliptic asymptotics for the first Painlevé transcendents",
  "authors": [
    "Shun Shimomura"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "For the first Painlev\\'e transcendents Kitaev established an asymptotic representation in terms of the Weierstrass pe-function in cheese-like strips near the point at infinity. We present an explicit error bound of this asymptotic expression, which leads to the order estimate of exponent $-1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-27T06:15:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34M55",
      "34M56",
      "34M40",
      "34M60",
      "33E05"
    ],
    "keywords": [
      "explicit error bound",
      "elliptic asymptotics",
      "first painleve transcendents kitaev",
      "asymptotic representation",
      "order estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}