{
  "id": "1105.2735",
  "version": "v3",
  "published": "2011-05-13T14:19:20.000Z",
  "updated": "2013-01-17T04:13:23.000Z",
  "title": "On a generalization of the generating function for Gegenbauer polynomials",
  "authors": [
    "Howard S. Cohl"
  ],
  "categories": [
    "math.CA",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "A generalization of the generating function for Gegenbauer polynomials is introduced whose coefficients are given in terms of associated Legendre functions of the second kind. We discuss how our expansion represents a generalization of several previously derived formulae such as Heine's formula and Heine's reciprocal square-root identity. We also show how this expansion can be used to compute hyperspherical harmonic expansions for power-law fundamental solutions of the polyharmonic equation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-01-17T04:13:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A08",
      "35J05",
      "32Q45",
      "31C12",
      "33C05",
      "42A16"
    ],
    "keywords": [
      "gegenbauer polynomials",
      "generating function",
      "generalization",
      "heines reciprocal square-root identity",
      "power-law fundamental solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.2735C"
    }
  }
}