{
  "id": "1305.2174",
  "version": "v1",
  "published": "2013-05-09T18:37:13.000Z",
  "updated": "2013-05-09T18:37:13.000Z",
  "title": "A gamma function in two variables",
  "authors": [
    "Mohamed El Bachraoui"
  ],
  "comment": "Submitted",
  "categories": [
    "math.NT"
  ],
  "abstract": "We introduce a gamma function $\\Ga(x,z)$ in two complex variables which extends the classical gamma function $\\Ga(z)$ in the sense that $\\lim_{x\\to 1}\\Ga(x,z)=\\Ga(z)$. We will show that many properties which $\\Ga(z)$ enjoys extend in a natural way to the function $\\Ga(x,z)$. Among other things we shall provide functional equations, a multiplication formula, and analogues of the Stirling formula with asymptotic estimates as consequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-09T18:37:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33B15",
      "11Y60",
      "11M06"
    ],
    "keywords": [
      "asymptotic estimates",
      "complex variables",
      "classical gamma function",
      "multiplication formula",
      "functional equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.2174E"
    }
  }
}