IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v305y2002i1p69-75.html
   My bibliography  Save this article

A new one-parameter deformation of the exponential function

Author

Listed:
  • Kaniadakis, G.
  • Scarfone, A.M.

Abstract

Recently, in Kaniadakis (Physica A 296 (2001) 405), a new one-parameter deformation for the exponential function exp{κ}(x)=(1+κ2x2+κx)1/κ; exp{0}(x)=exp(x), which presents a power-law asymptotic behaviour, has been proposed. The statistical distribution f=Z−1exp{κ}[−β(E−μ)], has been obtained both as stable stationary state of a proper nonlinear kinetics and as the state which maximizes a new entropic form. In the present contribution, starting from the κ-algebra and after introducing the κ-analysis, we obtain the κ-exponential exp{κ}(x) as the eigenstate of the κ-derivative and study its main mathematical properties.

Suggested Citation

  • Kaniadakis, G. & Scarfone, A.M., 2002. "A new one-parameter deformation of the exponential function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 69-75.
    • Handle: RePEc:eee:phsmap:v:305:y:2002:i:1:p:69-75
    DOI: 10.1016/S0378-4371(01)00642-2
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437101006422
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/S0378-4371(01)00642-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Atenas, Boris & Curilef, Sergio, 2021. "A statistical description for the Quasi-Stationary-States of the dipole-type Hamiltonian Mean Field Model based on a family of Vlasov solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    2. Abreu, Everton M.C. & Ananias Neto, Jorge & Mendes, Albert C.R. & de Paula, Rodrigo M., 2019. "Loop quantum gravity Immirzi parameter and the Kaniadakis statistics," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 307-310.
    3. Naudts, Jan, 2002. "Deformed exponentials and logarithms in generalized thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 323-334.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:305:y:2002:i:1:p:69-75. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.