{
  "id": "0903.0888",
  "version": "v1",
  "published": "2009-03-05T00:56:51.000Z",
  "updated": "2009-03-05T00:56:51.000Z",
  "title": "A note on additivity of polygamma functions",
  "authors": [
    "Feng Qi",
    "Bai-Ni Guo"
  ],
  "comment": "3 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "In the note, the functions $\\abs{\\psi^{(i)}(e^x)}$ for $i\\in\\mathbb{N}$ are proved to be sub-additive on $(\\ln\\theta_i,\\infty)$ and super-additive on $(-\\infty,\\ln\\theta_i)$, where $\\theta_i\\in(0,1)$ is the unique root of equation $2\\abs{\\psi^{(i)}(\\theta)}=\\abs{\\psi^{(i)}(\\theta^2)}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-05T00:56:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33B15",
      "26D07"
    ],
    "keywords": [
      "polygamma functions",
      "additivity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.0888Q"
    }
  }
}