{
  "id": "1203.5550",
  "version": "v1",
  "published": "2012-03-25T22:22:55.000Z",
  "updated": "2012-03-25T22:22:55.000Z",
  "title": "The perturbed Bessel equation, I. A Duality Theorem",
  "authors": [
    "V. P. Gurarii",
    "D. W. H. Gillam"
  ],
  "categories": [
    "math.CA",
    "math.FA"
  ],
  "abstract": "The Euler-Gauss linear transformation formula for the hypergeometric function was extended by Goursat for the case of logarithmic singularities. By replacing the perturbed Bessel differential equation by a monodromic functional equation, and studying this equation separately from the differential equation by an appropriate Laplace-Borel technique, we associate with the latter equation another monodromic relation in the dual complex plane. This enables us to prove a duality theorem and to extend Goursat's formula to much larger classes of functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-25T22:22:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perturbed bessel equation",
      "duality theorem",
      "euler-gauss linear transformation formula",
      "appropriate laplace-borel technique",
      "monodromic functional equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.5550G"
    }
  }
}