{
  "id": "1002.0083",
  "version": "v1",
  "published": "2010-01-30T19:55:55.000Z",
  "updated": "2010-01-30T19:55:55.000Z",
  "title": "Asymptotic expansions of several series and their application",
  "authors": [
    "Viktor P. Zastavnyi"
  ],
  "comment": "21 pages",
  "journal": "Ukrainian Mathematical Bulletin, vol. 6 (2009), N 4",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "Asymptotic expansions of series $\\sum_{k=0}^\\infty \\epsilon^k(k+a)^\\gamma e^{-(k+a)^\\alpha x}$ and $\\sum_{k=0}^\\infty \\epsilon^k(k+a)^\\gamma / (x(k+a)^\\alpha+1)^\\mu}$ in powers of $x$ as $x\\to+0$ are found, where $\\epsilon=1$ or $\\epsilon=-1$. These expansions are applied to obtain precise inequalities for Mathieu series. Keywords: Asymptotic expansion, residues, generalized Mathieu series, inequalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-30T19:55:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34E05",
      "26D15"
    ],
    "keywords": [
      "asymptotic expansion",
      "application",
      "generalized mathieu series"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}