{
  "id": "1806.03022",
  "version": "v1",
  "published": "2018-06-08T08:37:59.000Z",
  "updated": "2018-06-08T08:37:59.000Z",
  "title": "Combinatorial identities involving harmonic numbers",
  "authors": [
    "Necdet Batir"
  ],
  "comment": "submitted",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this work we prove a new combinatorial identity and applying it we establish many finite harmonic sum identities. Among many others, we prove that \\begin{equation*} \\sum_{k=1}^{n}\\frac{(-1)^{k-1}}{k}\\binom{n}{k}H_{n-k}=H_n^2+\\sum_{k=1}^{n}\\frac{(-1)^{k}}{k^2\\binom{n}{k}}, \\end{equation*} and \\begin{equation*} \\sum_{k=1}^{n}\\frac{(-1)^{k-1}}{k^2}\\binom{n}{k}H_{n-k}=\\frac{H_n[H_n^2+H_n^{(2)}]}{2}-\\sum_{k=0}^{n-1}\\frac{(-1)^k[H_n-H_k]}{(k+1)(n-k)\\binom{n}{k}}. \\end{equation*} Almost all of our results are new, while a few of them recapture know results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-08T08:37:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A10",
      "05A19"
    ],
    "keywords": [
      "combinatorial identity",
      "harmonic numbers",
      "finite harmonic sum identities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}