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Faculty of Architecture, Civil Engineering and Geodesy, University of Banja Luka , Banja Luka , Bosnia and Herzegovina
Department of Mathematics, Islamic Azad University, Karaj Branch , Karaj , Iran
Faculty of Architecture, Civil Engineering and Geodesy, University of Banja Luka , Banja Luka , Bosnia and Herzegovina
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.
Nested polynomials, Mittag-Leffler functions, Sturm-Liouville differential equation, Nested functions
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