Higher order Fibonacci and Lucas hypercomplex polynomials

In this thesis, the relationships between higher-order Fibonacci and Lucas polynomials and hypercomplex numbers are examined. The thesis study consists of four chapters. In the first chapter, which serves as the introduction, the historical development of the fundamental concepts used in the study and their interdisciplinary applications are discussed. Additionally, the main purpose of this thesis study is presented in this chapter. The second chapter includes a literature review related to the thesis topic, along with the fundamental definitions and theorems utilized in this study. In the third chapter, higher-order Fibonacci and Lucas hypercomplex polynomials are defined. Then, the Binet formulas and generating functions of these hypercomplex polynomials are given and many properties of these polynomials are presented in this section. The final chapter, Chapter Four, contains the conclusions of the thesis.