One type and second type chebyshev polynomials and chebyshev polynomial matrix sequences

In this thesis study, firstly some number sequences are defined and then Type I and Type II Chebyshev polynomial sequences and their properties are given. Then, by using these properties, a new matrix belonging to Type I and Type II Chebyshev polynomials is defined and various inequalities are obtained on these matrices and their proofs are shown using matrix algebra. Binet formula is defined for Type I and Type II Chebyshev polynomial matrix sequences and many theorems are proved by using this definition. Then, generator functions belonging to Type I and Type II Chebyshev polynomial matrix sequences are obtained. Partial and infinite sum formulas are obtained for Type I and Type II Chebyshev polynomial matrix sequences. In addition, exponential matrix sequence for Type II Chebyshev polynomial matrix sequences is shown using matrix algebra.