{
  "id": "1105.3689",
  "version": "v2",
  "published": "2011-05-18T17:06:05.000Z",
  "updated": "2015-03-30T17:33:50.000Z",
  "title": "The Binomial Coefficient for Negative Arguments",
  "authors": [
    "M. J. Kronenburg"
  ],
  "comment": "Corrected text on continuity",
  "categories": [
    "math.CO"
  ],
  "abstract": "The definition of the binomial coefficient in terms of gamma functions also allows non-integer arguments. For nonnegative integer arguments the gamma functions reduce to factorials, leading to the well-known Pascal triangle. Using a symmetry formula for the gamma function, this definition is extended to negative integer arguments, making the symmetry identity for binomial coefficients valid for all integer arguments. The agreement of this definition with some other identities and with the binomial theorem is investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-18T17:06:05.000Z",
      "abstract": "The definition of the binomial coefficient in terms of gamma functions also allows non-integer arguments. For nonnegative integer arguments the gamma functions reduce to factorials, leading to the well-known Pascal triangle. Using a symmetry formula for the gamma function, this definition is extended to negative integer arguments, making it continuous at all integer arguments. The agreement of this definition with some other identities and with the binomial theorem is investigated.",
      "comment": null,
      "journal": null,
      "doi": null,
      "authors": [
        "Maarten Kronenburg"
      ]
    },
    {
      "version": "v2",
      "updated": "2015-03-30T17:33:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "binomial coefficient",
      "negative arguments",
      "gamma functions reduce",
      "definition",
      "well-known pascal triangle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.3689K"
    }
  }
}