{
  "id": "2301.02141",
  "version": "v1",
  "published": "2023-01-05T16:34:42.000Z",
  "updated": "2023-01-05T16:34:42.000Z",
  "title": "A refinement of Lang's formula for the sum of powers of integers",
  "authors": [
    "José L. Cereceda"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In 2011, W. Lang derived a novel, explicit formula for the sum of powers of integers $S_k(n) = 1^k + 2^k + \\cdots + n^k$ involving simultaneously the Stirling numbers of the first and second kind. In this note, we first recall and then slightly refine Lang's formula for $S_k(n)$. As it turns out, the modified Lang's formula constitutes a special case of a general relationship discovered by Merca between the power sums, the elementary symmetric functions, and the complete homogeneous symmetric functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-05T16:34:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "refinement",
      "slightly refine langs formula",
      "complete homogeneous symmetric functions",
      "modified langs formula constitutes",
      "elementary symmetric functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}