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

Sunil Kumar Sharma, Waseem Ahmad Khan, Cheon-Seoung Ryoo and Ugur Duran
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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

Mathematics, 2022, vol. 10, issue 15, 1-18

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.

Keywords: ( p , q )-trigonometric functions; ( p , q )-calculus, cosine polynomials; sine polynomials; geometric polynomials; ( p , q )-geometric polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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