{
  "id": "2211.01148",
  "version": "v1",
  "published": "2022-11-01T17:29:58.000Z",
  "updated": "2022-11-01T17:29:58.000Z",
  "title": "On Infinite Series of Bessel functions of the First Kind: $\\sum_ν J_{Nν+p}(x), \\sum_ν(-1)^νJ_{Nν+p}(x)$",
  "authors": [
    "Suk Hyun Sung",
    "Robert Hovden"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Infinite series of Bessel function of the first kind, $\\sum_\\nu^{\\pm\\infty} J_{N\\nu+p}(x)$, $\\sum_\\nu^{\\pm\\infty} (-1)^\\nu J_{N\\nu+p}(x)$, are summed in closed form. These expressions are evaluated by engineering a Dirac comb that selects specific sequences within the Bessel series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-01T17:29:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first kind",
      "bessel function",
      "infinite series",
      "selects specific sequences",
      "bessel series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}