{
  "id": "2104.06568",
  "version": "v1",
  "published": "2021-04-14T00:54:53.000Z",
  "updated": "2021-04-14T00:54:53.000Z",
  "title": "A Summation of Series Involving Bessel Functions and Order Derivatives of Bessel Functions",
  "authors": [
    "Yilin Chen"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this note, we derive the closed-form expression for the summation of series $\\sum_{n=0}^{\\infty}nJ_n(x)\\partial J_n/\\partial n$, which is found in the calculation of entanglement entropy in 2-d bosonic free field, in terms of $Y_0$, $J_0$ and an integral involving these two Bessel functions. Further, we point out the integral can be expressed as a Meijer G function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-14T00:54:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bessel functions",
      "order derivatives",
      "bosonic free field",
      "closed-form expression",
      "entanglement entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}