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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
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    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.
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