On the properties of chebyshev polynomials

In this thesis, a detailed examination of the first, second, third and fourth kinds of Chebyshev polynomials and their properties have been made. Also, the relations of Chebyshev polynomials with special number sequences and polynomials of special number sequences are given. In the first section of this study, studies on Chebyshev polynomials are mentioned. In the second section, the basic definitions and theorems used throughout the thesis are given. In the third section, polynomials related to special number sequences are mentioned. In the fourth section, the basic properties of each kind of Chebyshev polynomials are given in detail. Again, the relations of Chebyshev polynomials with special number sequences and polynomials of special number sequences are given with examples. In this section, the relations of the first and second kind of Chebyshev polynomials with trigonometry are studied. Finally, in this section, shifted Chebyshev polynomials, which are different versions of Chebyshev polynomials, are examined for four kinds of Chebyshev polynomials. In the fifth chapter, derivatives and integrals of four different kinds of Chebyshev polynomials are given in detail. Finally, in the sixth section, the study is summarized, evaluations are made and some suggestions are given.