{
  "id": "1301.5432",
  "version": "v1",
  "published": "2013-01-23T08:38:30.000Z",
  "updated": "2013-01-23T08:38:30.000Z",
  "title": "Integral representations and summations of modified Struve function",
  "authors": [
    "Árpád Baricz",
    "Tibor K. Pogány"
  ],
  "comment": "18 pages, to appear in Acta Mathematica Hungarica",
  "journal": "Acta Mathematica Hungarica 141(3) (2013) 254-281",
  "doi": "10.1007/s10474-013-0308-x",
  "categories": [
    "math.CA"
  ],
  "abstract": "It is known that Struve function $\\mathbf H_\\nu$ and modified Struve function $\\mathbf L_\\nu$ are closely connected to Bessel function of the first kind $J_\\nu$ and to modified Bessel function of the first kind $I_\\nu$ and possess representations through higher transcendental functions like generalized hypergeometric ${}_1F_2$ and Meijer $G$ function. Also, the NIST project and Wolfram formula collection contain a set of Kapteyn type series expansions for $\\mathbf L_\\nu(x)$. In this paper firstly, we obtain various another type integral representation formulae for $\\mathbf L_\\nu(x)$ using the technique developed by D. Jankov and the authors. Secondly, we present some summation results for different kind of Neumann, Kapteyn and Schl\\\"omilch series built by $I_\\nu(x)$ and $\\mathbf L_\\nu(x)$ which are connected by a Sonin--Gubler formula, and by the associated modified Struve differential equation. Finally, solving a Fredholm type convolutional integral equation of the first kind, Bromwich--Wagner line integral expressions are derived for the Bessel function of the first kind $J_\\nu$ and for an associated generalized Schl\\\"omilch series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-23T08:38:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C10",
      "33E20",
      "40H05",
      "30B50",
      "40C10",
      "65B10"
    ],
    "keywords": [
      "modified struve function",
      "integral representation",
      "first kind",
      "modified struve differential equation",
      "bessel function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.5432B"
    }
  }
}