{
  "id": "1601.03167",
  "version": "v1",
  "published": "2016-01-13T08:32:38.000Z",
  "updated": "2016-01-13T08:32:38.000Z",
  "title": "Pick Functions Related to the Multiple Gamma Functions of order $n$",
  "authors": [
    "Sourav Das",
    "A. Swaminathan"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $G_n$ be the Barnes multiple Gamma function of order $n$ and the function $f_n(z)$ be defined as \\begin{align*} f_n(z)=\\dfrac{\\log G_n(z+1)}{z^n\\Log z},\\quad z\\in \\mathbb{C}\\setminus (-\\infty,0]. \\end{align*} In this work, a conjecture to find the Stieltjes representation is proposed such that $f_n(z)$ is a Pick function. The conjecture is established for the particular case $n=3$ by examining the properties of $f_3(z)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-13T08:32:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33B15",
      "41A60"
    ],
    "keywords": [
      "pick function",
      "barnes multiple gamma function",
      "conjecture",
      "stieltjes representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160103167D"
    }
  }
}