{
  "id": "1711.08368",
  "version": "v1",
  "published": "2017-10-23T21:38:24.000Z",
  "updated": "2017-10-23T21:38:24.000Z",
  "title": "Integral representations for the Fox-Wright functions with applications",
  "authors": [
    "Khaled Mehrez"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Our aim in this paper is to derive several new integral representations of the Fox-Wright functions. In particular, we give new Laplace and Stieltjes transform for this special functions under a special restriction on parameters. From the positivity conditions for the weight in these representations, we found sufficient conditions to be imposed on the parameters of the Fox-Wright functions that it be completely monotonic. As applications, we extended Luke's inequalities and we present new Tur\\'an type inequalities for the Fox-Wright function. Finally, by appealing to each of the Luke's inequalities, two sets of two-sided bounding inequalities for the generalized Mathieu's type series are proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-23T21:38:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fox-wright function",
      "integral representations",
      "applications",
      "turan type inequalities",
      "generalized mathieus type series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}