{
  "id": "2203.09787",
  "version": "v1",
  "published": "2022-03-18T08:08:49.000Z",
  "updated": "2022-03-18T08:08:49.000Z",
  "title": "A New Probabilistic Representation of the Alternating Zeta Function and a New Selberg-like Integral Evaluation",
  "authors": [
    "Serge Iovleff"
  ],
  "categories": [
    "math.CA",
    "math.PR"
  ],
  "abstract": "In this paper, we present two new representations of the alternating Zeta function. We show that for any s $\\in$ C this function can be computed as a limit of a series of determinant. We then express these determinants as the expectation of a functional of a random vector with Dixon-Anderson density. The generalization of this representation to more general alternating series allows us to evaluate a Selberg-type integral with a generalized Vandermonde determinant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-18T08:08:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "alternating zeta function",
      "selberg-like integral evaluation",
      "probabilistic representation",
      "generalized vandermonde determinant",
      "selberg-type integral"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}