Bicomplex-complex Leonardo numbers

The purpose of this thesis is to introduce bicomplex-complex Leonardo numbers and to examine some properties of these numbers. This thesis consists of four chapters. In the first chapter, some studies that shed light on our study are mentioned. In the second chapter, some essential definitions and theorems that form the basis of our study are given. In the third chapter, at first, bicomplex-complex Leonardo numbers are defined and some fundamental properties of these numbers are obtained. Then, recurrence relations, Binet's formula, generating function and some summations formulas for bicomplex-complex Leonardo numbers are given. Catalan's identity, Cassini's identity, d'Ocagne's identity, Honsberger's identity and Vajda's identity involving bicomplex-complex Leonardo numbers are derived. In addition, some other identites involving bicomplex-complex Leonardo numbers are obtained. In the last chapter, some results obtained from the thesis and some suggestions are presented.