IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i6p955-d1611774.html
   My bibliography  Save this article

Insights into New Generalization of q -Legendre-Based Appell Polynomials: Properties and Quasi Monomiality

Author

Listed:
  • Naeem Ahmad

    (Mathematics Department, College of Science, Jouf University, Sakaka 72388, Saudi Arabia)

  • Waseem Ahmad Khan

    (Department of Electrical Engineering, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia)

Abstract

In this paper, by using the zeroth-order q -Tricomi functions, the theory of three-variable q -Legendre-based Appell polynomials is introduced. These polynomials are studied by means of generating functions, series expansions, and determinant representation. Further, by utilizing the concepts of q -quasi-monomiality, these polynomials are examined as several q -quasi-monomial and operational representations; the q -differential equations for the three-variable q -Legendre-based Appell polynomials were obtained. In addition, we established a new generalization of three-variable q -Legendre-Hermite-Appell polynomials, and we derive series expansion, determinant representation, and q -quasi-monomial and q -differential equations. Some examples are framed to better illustrate the theory of three-variable q -Legendre-based Appell polynomials, and this is characterized by the above properties.

Suggested Citation

  • Naeem Ahmad & Waseem Ahmad Khan, 2025. "Insights into New Generalization of q -Legendre-Based Appell Polynomials: Properties and Quasi Monomiality," Mathematics, MDPI, vol. 13(6), pages 1-17, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:955-:d:1611774
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/6/955/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/6/955/
    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:13:y:2025:i:6:p:955-:d:1611774. 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.