IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i12p2154-d455573.html
   My bibliography  Save this article

Explicit Construction of the Inverse of an Analytic Real Function: Some Applications

Author

Listed:
  • Joaquín Moreno

    (Department of Applied Mathematics, Superior Technical School of Building Engineering, Polytechnic University of Valencia, 46022 Valencia, Spain)

  • Miguel A. López

    (SIDIS Research Group, Department of Mathematics and Institute of Applied Mathematics in Science and Engineering (IMACI), Polytechnic School of Cuenca, University of Castilla-La Mancha, 16071 Cuenca, Spain)

  • Raquel Martínez

    (SIDIS Research Group, Department of Mathematics and Institute of Applied Mathematics in Science and Engineering (IMACI), Polytechnic School of Cuenca, University of Castilla-La Mancha, 16071 Cuenca, Spain)

Abstract

In this paper, we introduce a general procedure to construct the Taylor series development of the inverse of an analytical function; in other words, given y = f ( x ) , we provide the power series that defines its inverse x = h f ( y ) . We apply the obtained results to solve nonlinear equations in an analytic way, and generalize Catalan and Fuss–Catalan numbers.

Suggested Citation

  • Joaquín Moreno & Miguel A. López & Raquel Martínez, 2020. "Explicit Construction of the Inverse of an Analytic Real Function: Some Applications," Mathematics, MDPI, vol. 8(12), pages 1-23, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2154-:d:455573
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/12/2154/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/12/2154/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:8:y:2020:i:12:p:2154-:d:455573. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.