{
  "id": "1710.01270",
  "version": "v1",
  "published": "2017-10-03T16:38:22.000Z",
  "updated": "2017-10-03T16:38:22.000Z",
  "title": "A Gronwall-type Trigonometric Inequality",
  "authors": [
    "A. G. Smirnov"
  ],
  "comment": "To appear in the American Mathematical Monthly",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "We prove that the absolute value of the $n$th derivative of $\\cos(\\sqrt{x})$ does not exceed $n!/(2n)!$ for all $x>0$ and $n = 0,1,\\ldots$ and obtain a natural generalization of this inequality involving the analytic continuation of $\\cos(\\sqrt{x})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-03T16:38:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D05"
    ],
    "keywords": [
      "gronwall-type trigonometric inequality",
      "absolute value",
      "natural generalization",
      "analytic continuation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}