{
  "id": "1410.5043",
  "version": "v1",
  "published": "2014-10-19T07:03:20.000Z",
  "updated": "2014-10-19T07:03:20.000Z",
  "title": "On the integral representations of $|Γ(z)|^2$ and its Fourier transform",
  "authors": [
    "Nicolas Privault"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We derive integral representations in terms of the Macdonald functions for the square modulus $s\\mapsto | \\Gamma ( a + i s ) |^2$ of the Gamma function and its Fourier transform when $a<0$ and $a\\not= -1,-2,\\ldots $, generalizing known results in the case $a>0$. This representation is based on a renormalization argument using modified Bessel functions of the second kind, and it applies to the representation of the solutions of the Fokker-Planck equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-19T07:03:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fourier transform",
      "gamma function",
      "square modulus",
      "macdonald functions",
      "derive integral representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.5043P"
    }
  }
}