{
  "id": "2207.09451",
  "version": "v1",
  "published": "2022-07-13T05:09:38.000Z",
  "updated": "2022-07-13T05:09:38.000Z",
  "title": "Balancing polynomials, Fibonacci numbers and some new series for $π$",
  "authors": [
    "Robert Frontczak",
    "Kalika Prasad"
  ],
  "comment": "16 pages, 5 tables",
  "categories": [
    "math.NT",
    "cs.DM",
    "math.CO"
  ],
  "abstract": "We evaluate some types of infinite series with balancing and Lucas-balancing polynomials in closed form. These evaluations will lead to some new curious series for $\\pi$ involving Fibonacci and Lucas numbers. Our findings complement those of Castellanos from 1986 and 1989.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-13T05:09:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B37",
      "11B39",
      "15A15"
    ],
    "keywords": [
      "fibonacci numbers",
      "infinite series",
      "lucas numbers",
      "findings complement",
      "castellanos"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}