{
  "id": "2404.11173",
  "version": "v1",
  "published": "2024-04-17T08:42:42.000Z",
  "updated": "2024-04-17T08:42:42.000Z",
  "title": "A simple derivation of the integrals of products of Legendre polynomials with logarithmic weight",
  "authors": [
    "Sebastian Schmutzhard-Höfler"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We explore integrals of products of Legendre polynomials with a logarithmic weight function. More precisely, for Legendre polynomials $P_m$ and $P_n$ of orders $m$ and $n$, respectively, we provide simple derivations of the integrals $$\\int \\limits_0^1 P_n(2x-1) P_m(2x-1)\\log (x)dx.$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-17T08:42:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "legendre polynomials",
      "simple derivation",
      "logarithmic weight function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}