Oresme numbers and applications

In this study, Oresme numbers are discussed and the thesis consists of four parts. In the first chapter, Oresme numbers are mentioned and the places where they are used and the literature review are included. In the second chapter, the geometric interpretation of Oresme numbers is made. Additionally, while examining the geometric part in this section, its relationship with generalized Fibonacci numbers is also mentioned. In the following, k- Oresme numbers, which are the generalization of these numbers, and negative indices k- Oresme numbers are discussed. The important identities of these numbers are given with the help of the matrix. In addition, polynomials are given as generalizations of the newly defined negative indices k- Oresme numbers. These numbers and polynomials have been studied in detail. In the last section, k- Oresme Hybrid numbers were examined. The closed formula and generator function of these numbers are given. Some well known important identities and sum formulas have been obtained for these newly defined numbers in the literature.