{
  "id": "2205.03545",
  "version": "v1",
  "published": "2022-05-07T04:16:10.000Z",
  "updated": "2022-05-07T04:16:10.000Z",
  "title": "Inverse Laplace transform based on Widder's method for Tsallis exponential",
  "authors": [
    "S. S. Naina Mohammed",
    "K. Jeevanandham",
    "A. Basheerrudin Mahmud Ahmed",
    "Md. Manirul Ali",
    "R. Chandrashekar R. Chandrashekar"
  ],
  "comment": "20 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "A generalization of the Laplace transform based on the generalized Tsallis $q$-exponential is given in the present work for a new type of kernel. We also define the inverse transform for this generalized transform based on the complex integration method. We prove some identities corresponding to the Laplace transform and inverse transform like the $q$-convolution theorem, the action of generalized derivative and generalized integration on the Laplace transform. We then derive a $q$-generalization of the inverse Laplace transform based on the Post-Widders method which bypasses the necessity for a complex contour integration. We demonstrate the usefulness of this in computing the Laplace and inverse Laplace transform of some elementary functions. Finally we use the Post-Widder's method based inverse Laplace transform to compute the density of states from the partition function for the case of a generalized ideal gas in three dimensions as also for a linear harmonic oscillator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-07T04:16:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse laplace transform",
      "tsallis exponential",
      "inverse transform",
      "post-widders method",
      "linear harmonic oscillator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}