{
  "id": "1310.8269",
  "version": "v1",
  "published": "2013-10-30T19:05:52.000Z",
  "updated": "2013-10-30T19:05:52.000Z",
  "title": "Fourier transform of a Bessel function multiplied by a Gaussian",
  "authors": [
    "Michael Carley"
  ],
  "comment": "Submitted to Journal of Physics A",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "An analytical result is given for the exact evaluation of an integral which arises in the analysis of acoustic radiation from wave packet sources: $ I_{mn}(\\beta,q) = \\int_{-\\infty}^{\\infty} e^{-\\beta^{2}x^{2}-i q x}x^{m+1/2}J_{n+1/2}(x) \\,d x, $ where $m$ and $n$ are non-negative integers, and $J_{n+1/2}(\\cdot)$ is a Bessel function of order $n+1/2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-30T19:05:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bessel function",
      "fourier transform",
      "wave packet sources",
      "acoustic radiation",
      "exact evaluation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.8269C"
    }
  }
}