IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i24p4978-d1301665.html
   My bibliography  Save this article

On Some Formulas for the Lauricella Function

Author

Listed:
  • Ainur Ryskan

    (Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, 86 Tole Bi Street, Almaty 050012, Kazakhstan
    These authors contributed equally to this work.)

  • Tuhtasin Ergashev

    (Department of Higher Mathematics, National Research University “TIIAME”, 39 Kari-Niyazi Street, Tashkent 100000, Uzbekistan
    Department of Mathematics, Analysis, Logic and Discrete Mathematics, Ghent University, 9000 Gent, Belgium
    These authors contributed equally to this work.)

Abstract

Lauricella, G. in 1893 defined four multidimensional hypergeometric functions F A , F B , F C and F D . These functions depended on three variables but were later generalized to many variables. Lauricella’s functions are infinite sums of products of variables and corresponding parameters, each of them has its own parameters. In the present work for Lauricella’s function F A ( n ) , the limit formulas are established, some expansion formulas are obtained that are used to write recurrence relations, and new integral representations and a number of differentiation formulas are obtained that are used to obtain the finite and infinite sums. In the presentation and proof of the obtained formulas, already known expansions and integral representations of the considered F A ( n ) function, definitions of gamma and beta functions, and the Gaussian hypergeometric function of one variable are used.

Suggested Citation

  • Ainur Ryskan & Tuhtasin Ergashev, 2023. "On Some Formulas for the Lauricella Function," Mathematics, MDPI, vol. 11(24), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4978-:d:1301665
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/24/4978/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/24/4978/
    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:11:y:2023:i:24:p:4978-:d:1301665. 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.