On Gaussian Pell quaternion polynomials

Among integer sequences, Fibonacci sequence is the most studied integer sequences. On the other hand, Pell number sequence and generalizations of this sequence have been studied by many authors. The main purpose of this thesis is to introduce Gaussian Pell quaternion polynomials with Gaussian Pell polynomial components and to examine some properties of them. This thesis consists of four chapters. In the first chapter, some concepts involving our study are mentioned and some current studies that inspired our study are given. In the second chapter, definitions and theorems that form the basis of our study are presented. In the third chapter, at first, Gaussian Pell quaternion polynomials are introduced. Then some algebraic properties including recurrence relation, Binet's formula, (ordinary) generating function, exponential generating function and Poisson generating function of the Gaussian Pell quaternion polynomials are given. Moreover, some identities related to the Gaussian Pell quaternion polynomials are obtained. In the last chapter, some results obtained from the thesis are emphasized and some suggestions are given.