Euler numbers, polynomals and properties


Thesis Type: Postgraduate

Institution Of The Thesis: Uludağ Üniversitesi, Turkey

Approval Date: 2010

Thesis Language: Turkish

Student: HATİCE ÖZBAY

Supervisor: İSMAİL NACİ CANGÜL

Abstract:

In this thesis, several properties and usage areas of Euler numbers and polynomials are given. The thesis consists of three chapters. In the first chapter, the preliminary notions which are to be used in later chapters are given. In the second chapter Euler numbers and polynomials are defined and relations to calculate them are considered. Also some properties of Euler numbers and polynomials and the relations between these numbers and polynomials are given. Finally the zeta functions of these numbers are studied and the relation between Euler numbers and Bernoulli numbers is given. In the third chapter, some further properties of Euler numbers and polynomials are given and especially, their congruences in the moduli powers of two are studied.