IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v307y2017icp204-216.html
   My bibliography  Save this article

Generalized Humbert polynomials via generalized Fibonacci polynomials

Author

Listed:
  • Wang, Weiping
  • Wang, Hui

Abstract

In this paper, we define the generalized (p, q)-Fibonacci polynomials un, m(x) and generalized (p, q)-Lucas polynomials vn, m(x), and further introduce the generalized Humbert polynomials un,m(r)(x) as the convolutions of un, m(x). We give many expressions, expansions, recurrence relations and differential recurrence relations of un,m(r)(x), and study the matrices and determinants related to the polynomials un, m(x), vn, m(x) and un,m(r)(x). Finally, we present an algebraic interpretation for the generalized Humbert polynomials un,m(r)(x). It can be found that various well-known polynomials are special cases of un, m(x), vn, m(x) or un,m(r)(x). Therefore, by introducing the general polynomials un, m(x), vn, m(x) and un,m(r)(x), we have a unified approach to dealing with many special polynomials in the literature.

Suggested Citation

  • Wang, Weiping & Wang, Hui, 2017. "Generalized Humbert polynomials via generalized Fibonacci polynomials," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 204-216.
    • Handle: RePEc:eee:apmaco:v:307:y:2017:i:c:p:204-216
    DOI: 10.1016/j.amc.2017.02.050
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317301613
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.02.050?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nalli, Ayse & Haukkanen, Pentti, 2009. "On generalized Fibonacci and Lucas polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3179-3186.
    2. Djordjević, Gospava B. & Djordjević, Snežana S., 2015. "Convolutions of the generalized Morgan–Voyce polynomials," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 106-115.
    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. Yuankui Ma & Wenpeng Zhang, 2018. "Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers," Mathematics, MDPI, vol. 6(12), pages 1-8, December.
    2. Florek, Wojciech, 2018. "A class of generalized Tribonacci sequences applied to counting problems," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 809-821.

    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. 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.
    2. Catarino, Paula, 2015. "A note on h(x) − Fibonacci quaternion polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 1-5.
    3. Flaut, Cristina & Shpakivskyi, Vitalii & Vlad, Elena, 2017. "Some remarks regarding h(x) – Fibonacci polynomials in an arbitrary algebra," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 32-35.

    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:eee:apmaco:v:307:y:2017:i:c:p:204-216. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.