{
  "id": "1301.3039",
  "version": "v2",
  "published": "2013-01-11T11:49:48.000Z",
  "updated": "2014-01-22T15:39:02.000Z",
  "title": "On the definite integral of two confluent hypergeometric functions related to the Kampé de Fériet double series",
  "authors": [
    "Rytis Jursenas"
  ],
  "comment": "14 pages, accepted for publication in Lith Math J",
  "categories": [
    "math.CA"
  ],
  "abstract": "The Kamp\\'{e} de F\\'{e}riet double series $F_{1:1;1}^{1:1;1}$ is studied through the solution to the associated first-order nonhomogeneous differential equation. It is shown that the integral of $t^{\\beta+l}M(\\cdot;\\beta;\\lambda t)M(\\cdot;\\beta;-\\lambda t)$ over $t\\in[0,T]$, $T\\geq0$, $l=0,1,\\ldots$, $\\Re\\beta+l>-1$, is a linear combination of functions $F_{1:1;1}^{1:1;1}$. The integral is a generalization of a class of so-called Coulomb integrals involving regular Coulomb wave functions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-22T15:39:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C15",
      "33C20",
      "33C60"
    ],
    "keywords": [
      "confluent hypergeometric functions",
      "fériet double series",
      "definite integral",
      "regular coulomb wave functions",
      "associated first-order nonhomogeneous differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.3039J"
    }
  }
}