IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i13p2342-d855534.html
   My bibliography  Save this article

Novel Results for Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals

Author

Listed:
  • Waleed Mohamed Abd-Elhameed

    (Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt)

  • Andreas N. Philippou

    (Department of Mathematics, University of Patras, 26504 Patras, Greece)

  • Nasr Anwer Zeyada

    (Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
    Department of Mathematics, College of Science, University of Jeddah, Jeddah 23218, Saudi Arabia)

Abstract

The goal of this study is to develop some new connection formulae between two generalized classes of Fibonacci and Lucas polynomials. Hypergeometric functions of the kind 2 F 1 ( z ) are included in all connection coefficients for a specific z . Several new connection formulae between some famous polynomials, such as Fibonacci, Lucas, Pell, Fermat, Pell–Lucas, and Fermat–Lucas polynomials, are deduced as special cases of the derived connection formulae. Some of the introduced formulae generalize some of those existing in the literature. As two applications of the derived connection formulae, some new formulae linking some celebrated numbers are given and also some newly closed formulae of certain definite weighted integrals are deduced. Based on using the two generalized classes of Fibonacci and Lucas polynomials, some new reduction formulae of certain odd and even radicals are developed.

Suggested Citation

  • Waleed Mohamed Abd-Elhameed & Andreas N. Philippou & Nasr Anwer Zeyada, 2022. "Novel Results for Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals," Mathematics, MDPI, vol. 10(13), pages 1-18, July.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2342-:d:855534
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/13/2342/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/13/2342/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ye, Xiaoli & Zhang, Zhizheng, 2017. "A common generalization of convolved generalized Fibonacci and Lucas polynomials and its applications," Applied Mathematics and Computation, Elsevier, vol. 306(C), pages 31-37.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Mei Bai & Wenchang Chu & Dongwei Guo, 2022. "Reciprocal Formulae among Pell and Lucas Polynomials," Mathematics, MDPI, vol. 10(15), pages 1-11, July.
    2. Waleed Mohamed Abd-Elhameed & Amr Kamel Amin, 2023. "Novel Formulas of Schröder Polynomials and Their Related Numbers," Mathematics, MDPI, vol. 11(2), pages 1-23, January.
    3. Dongwei Guo & Wenchang Chu, 2022. "Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers," Mathematics, MDPI, vol. 10(15), pages 1-10, July.
    4. Waleed Mohamed Abd-Elhameed, 2022. "Novel Formulae of Certain Generalized Jacobi Polynomials," Mathematics, MDPI, vol. 10(22), pages 1-25, November.

    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.
    1. Yang, Jizhen & Zhang, Zhizheng, 2018. "Some identities of the generalized Fibonacci and Lucas sequences," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 451-458.
    2. Yuankui Ma & Wenpeng Zhang, 2018. "Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers," Mathematics, MDPI, vol. 6(12), pages 1-8, December.
    3. W. M. Abd-Elhameed & N. A. Zeyada, 2022. "New formulas including convolution, connection and radicals formulas of k-Fibonacci and k-Lucas polynomials," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 1006-1016, December.

    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:13:p:2342-:d:855534. 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.