{
  "id": "2210.14693",
  "version": "v1",
  "published": "2022-10-26T13:23:40.000Z",
  "updated": "2022-10-26T13:23:40.000Z",
  "title": "On the positivity of a certain function related with the Digamma function",
  "authors": [
    "K. Castillo"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "It is proved that $$\\left(\\frac{x^n}{1-e^{-x}}\\right)^{(n)}>0$$ for all $x\\in (\\log 2, \\infty)$ and $n\\in \\mathbb{N}$, which improves the result of [Al-Musallam and Bustoz in Ramanujan J. 11 (2006) 399-402].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-26T13:23:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "digamma function",
      "positivity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}