IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i4p556-d746793.html
   My bibliography  Save this article

Generalized q -Difference Equations for q -Hypergeometric Polynomials with Double q -Binomial Coefficients

Author

Listed:
  • Jian Cao

    (School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China)

  • Hari M. Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan
    Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy)

  • Hong-Li Zhou

    (School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China)

  • Sama Arjika

    (Department of Mathematics and Informatics, University of Agadez, Agadez P.O. Box 199, Niger
    International Chair of Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi, P.O. Box 072, Cotonou 50, Benin)

Abstract

In this paper, we apply a general family of basic (or q -) polynomials with double q -binomial coefficients as well as some homogeneous q -operators in order to construct several q -difference equations involving seven variables. We derive the Rogers type and the extended Rogers type formulas as well as the Srivastava-Agarwal-type bilinear generating functions for the general q -polynomials, which generalize the generating functions for the Cigler polynomials. We also derive a class of mixed generating functions by means of the aforementioned q -difference equations. The various results, which we have derived in this paper, are new and sufficiently general in character. Moreover, the generating functions presented here are potentially applicable not only in the study of the general q -polynomials, which they have generated, but indeed also in finding solutions of the associated q -difference equations. Finally, we remark that it will be a rather trivial and inconsequential exercise to produce the so-called ( p , q ) -variations of the q -results, which we have investigated here, because the additional forced-in parameter p is obviously redundant.

Suggested Citation

  • Jian Cao & Hari M. Srivastava & Hong-Li Zhou & Sama Arjika, 2022. "Generalized q -Difference Equations for q -Hypergeometric Polynomials with Double q -Binomial Coefficients," Mathematics, MDPI, vol. 10(4), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:556-:d:746793
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/4/556/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/4/556/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yun Zhou & Qiu-Ming Luo, 2014. "Some New Generating Functions for -Hahn Polynomials," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-5, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:10:y:2022:i:4:p:556-:d:746793. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.