{
  "id": "math/0310063",
  "version": "v1",
  "published": "2003-10-06T00:31:46.000Z",
  "updated": "2003-10-06T00:31:46.000Z",
  "title": "Coupling of the Legendre polynomials with kernels $|x-y|^α$ and $\\ln|x-y|$",
  "authors": [
    "S. Sadov"
  ],
  "comment": "23 pp. LaTeX, Preprint of the Keldysh Institute for Applied Mathematics",
  "categories": [
    "math.CA"
  ],
  "abstract": "Double integrals that represent matrix elements of the power and logarithmic potentials in the Legendre polynoiomial basis on [-1,1] are found in a closed form. Several proofs are given, which involve different special functions and identities. A connection of the new formulae and Whipple's hypergeometric summation formula is shown.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-06T00:31:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C20",
      "45H05"
    ],
    "keywords": [
      "legendre polynomials",
      "whipples hypergeometric summation formula",
      "represent matrix elements",
      "legendre polynoiomial basis",
      "special functions"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10063S"
    }
  }
}