IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i15p2709-d876970.html
   My bibliography  Save this article

Diverse Properties and Approximate Roots for a Novel Kinds of the ( p , q )-Cosine and ( p , q )-Sine Geometric Polynomials

Author

Listed:
  • Sunil Kumar Sharma

    (Department of Information Technology, College of Computer and Information Sciences, Majmaah University, Al-Majmaah 11952, Saudi Arabia)

  • Waseem Ahmad Khan

    (Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia)

  • Cheon-Seoung Ryoo

    (Department of Mathematics, Hannam University, Daejeon 34430, Korea)

  • Ugur Duran

    (Department of Basic Sciences of Engineering, İskenderun Technical University, Hatay 31200, Turkey)

Abstract

Utilizing p , q -numbers and p , q -concepts, in 2016, Duran et al. considered p , q -Genocchi numbers and polynomials, p , q -Bernoulli numbers and polynomials and p , q -Euler polynomials and numbers and provided multifarious formulas and properties for these polynomials. Inspired and motivated by this consideration, many authors have introduced ( p , q ) -special polynomials and numbers and have described some of their properties and applications. In this paper, using the ( p , q ) -cosine polynomials and ( p , q ) -sine polynomials, we consider a novel kinds of ( p , q ) -extensions of geometric polynomials and acquire several properties and identities by making use of some series manipulation methods. Furthermore, we compute the p , q -integral representations and p , q -derivative operator rules for the new polynomials. Additionally, we determine the movements of the approximate zerosof the two mentioned polynomials in a complex plane, utilizing the Newton method, and we illustrate them using figures.

Suggested Citation

  • Sunil Kumar Sharma & Waseem Ahmad Khan & Cheon-Seoung Ryoo & Ugur Duran, 2022. "Diverse Properties and Approximate Roots for a Novel Kinds of the ( p , q )-Cosine and ( p , q )-Sine Geometric Polynomials," Mathematics, MDPI, vol. 10(15), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2709-:d:876970
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/15/2709/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/15/2709/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Khristo N. Boyadzhiev, 2005. "A series transformation formula and related polynomials," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-18, January.
    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.
    1. Sunil Kumar Sharma & Waseem A. Khan & Cheon Seoung Ryoo, 2020. "A Parametric Kind of Fubini Polynomials of a Complex Variable," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    2. Manuel D. Ortigueira, 2022. "A New Series Representation and the Laplace Transform for the Lognormal Distribution," Mathematics, MDPI, vol. 10(19), pages 1-13, September.
    3. Hacène Belbachir & Yahia Djemmada, 2020. "Generalized Geometric Polynomials Via Steffensen’s Generalized Factorials and Tanny’s Operators," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1713-1727, December.
    4. Khristo N. Boyadzhiev, 2011. "Series transformation formulas of Euler type, Hadamard product of series, and harmonic number identities," Indian Journal of Pure and Applied Mathematics, Springer, vol. 42(5), pages 371-386, October.

    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:15:p:2709-:d:876970. 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.