On derivatives and integrals of Fibonacci and Chebyshev polynomials

The derivatives and integrals of Fibonacci polynomials and Chebyshev polynomials have both been thoroughly examined in this thesis. In this sense, by examining the Fibonacci and Chebyshev polynomials, the identities in the literature related to the derivatives and integrals of these polynomials have been investigated. In addition, in this thesis, the relationship between Fibonacci polynomials and Pascal's triangle is given. The researches on the thesis subject are mentioned in the first section of this study, which consists of five sections. Fundamental knowledge regarding the study, definitions, and theorems are provided in the second section. Fibonacci polynomials are fully examined in the third section. Fibonacci polynomial identities, their first and second derivatives, and their integrals are investigated. The fourth section provides detailed information on the derivatives and integrals of four different kinds of Chebyshev polynomials. The relationships between the first and second kinds of Chebyshev polynomials and trigonometry are also shown. The study was summarized, evaluated, and some recommendations for future research were made in the fifth section, which is titled Conclusion and Suggestions.