{
  "id": "2105.03794",
  "version": "v1",
  "published": "2021-05-08T22:46:10.000Z",
  "updated": "2021-05-08T22:46:10.000Z",
  "title": "On the coefficients in an asymptotic expansion of $(1+1/x)^x$",
  "authors": [
    "T. M. Dunster",
    "Jessica M. Perez"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "The function $g(x)= (1+1/x)^{x}$ has the well-known limit $e$ as $x\\rightarrow{\\infty}$. The coefficients $c_{j}$ in an asymptotic expansion for $g(x)$ are considered. A simple recursion formula is derived, and then using Cauchy's integral formula the coefficients are approximated for large $j$. From this it is shown that $|c_{j}|\\rightarrow{1}$ as $j\\rightarrow{\\infty}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-08T22:46:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A58",
      "30E15",
      "30E20"
    ],
    "keywords": [
      "asymptotic expansion",
      "coefficients",
      "cauchys integral formula",
      "simple recursion formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}