{
  "id": "1511.06612",
  "version": "v1",
  "published": "2015-11-20T14:35:09.000Z",
  "updated": "2015-11-20T14:35:09.000Z",
  "title": "Some new facts around the delta neutral H function of Fox",
  "authors": [
    "D. Karp",
    "E. Prilepkina"
  ],
  "comment": "21 page, no figures",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "In this paper we find several new properties of delta neutral H function of Fox. In particular, we find expansion in the neighborhood of finite nonzero singularity and give new Mellin transform formulas under a special restriction on parameters. The last result is applied to prove a conjecture regarding the representing measure for gamma ratio in Bernstein's theorem. Further, we find weak limit of measures expressed in terms of H function providing a regularization method for integrals containing delta neutral zero-balanced H function. We apply this result to extend a recently discovered integral equation to zero-balanced case. In the last section we consider this integral equation in case of Meijer's G function which leads to certain expansions believed to be new even in the case of the Gauss hypergeometric function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-20T14:35:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C60",
      "33C05"
    ],
    "keywords": [
      "integral equation",
      "gauss hypergeometric function",
      "mellin transform formulas",
      "integrals containing delta neutral",
      "finite nonzero singularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151106612K"
    }
  }
}