{
  "id": "2112.07382",
  "version": "v2",
  "published": "2021-12-14T13:21:19.000Z",
  "updated": "2022-07-24T10:03:22.000Z",
  "title": "Revisiting the Coulomb problem: A novel representation of the confluent hypergeometric function as an infinite sum of discrete Bessel functions",
  "authors": [
    "A. D. Alhaidari"
  ],
  "comment": "7 pages, 1 table, 2 figures; improved version",
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We use the tridiagonal representation approach to solve the radial Schr\\\"odinger equation for the continuum scattering states of the Coulomb problem in a complete basis set of discrete Bessel functions. Consequently, we obtain a new representation of the confluent hypergeometric function as an infinite sum of Bessel functions, which is numerically very stable and more rapidly convergent than another well-known formula.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-07-24T10:03:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "confluent hypergeometric function",
      "discrete bessel functions",
      "infinite sum",
      "coulomb problem",
      "novel representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}