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Vol 16, Issue 1, 2024
Pages: 785 - 792
Research paper
Other Editor: Stepgrad Conference
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Published: 12.06.2024. Research paper Other Editor: Stepgrad Conference

NESTED POLYNOMIALS TRIGONOMETRIC AND HYPERBOLIC TYPE WITH APPLICATIONS

By
Snježana Maksimović ,
Snježana Maksimović

Faculty of Architecture, Civil Engineering and Geodesy, University of Banja Luka , Banja Luka, Bosnia and Herzegovina

Arslan Ansari ,
Arslan Ansari

Department of Mathematics, Islamic Azad University, Karaj Branch, Karaj, Iran

Sandra Kosić-Jeremić
Sandra Kosić-Jeremić
Contact Sandra Kosić-Jeremić

Faculty of Architecture, Civil Engineering and Geodesy, University of Banja Luka, Banja Luka, Bosnia and Herzegovina

Abstract

In this paper we introduce nested trigonometric and hyperbolic polynomials of rank n by employing nested trigonometric and hyperbolic functions, respectively. Our investigation delves into some interesting properties of nested polynomials, establishing some recurrence formulas and deriving some useful summation formulas. Additionally, we establish a connection between nested trigonometric polynomials and one specific class of special polynomials that satisfy a second-order Sturm-Liouville differential equation. Finally, we outline several applications of nested polynomials. Among others, it is shown that nested trigonometric polynomials can be used for the linear static analysis of curved Bernoulli–Euler beam.

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