{
  "id": "1606.02008",
  "version": "v1",
  "published": "2016-06-07T03:09:09.000Z",
  "updated": "2016-06-07T03:09:09.000Z",
  "title": "A new type of sharp bounds for ratios of modified Bessel functions",
  "authors": [
    "D. Ruiz-Antolin",
    "J. Segura"
  ],
  "comment": "To appear in J. Math. Anal. Appl",
  "categories": [
    "math.CA"
  ],
  "abstract": "The bounds for the ratios of first and second kind modified Bessel functions of consecutive orders are important quantities appearing in a large number of scientific applications. We obtain new bounds which are accurate in a large region of parameters and which are shaper than previous bounds. The new bounds are obtained by a qualitative analysis of the Riccati equation satisfied by these ratios. A procedure is considered in which the bounds obtained from the analysis of the Riccati equation are used to define a new function satisfying a new Riccati equation which yields sharper bounds. Similar ideas can be applied to other functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-07T03:09:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C10",
      "26D07"
    ],
    "keywords": [
      "sharp bounds",
      "riccati equation",
      "second kind modified bessel functions",
      "yields sharper bounds",
      "scientific applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}