## Bernoulli numbers, poynomials and properties

Institution Of The Thesis: Uludağ Üniversitesi, Turkey

Approval Date: 2009

Thesis Language: Turkish

Student: MÜGE ÇAPKIN

Supervisor: İSMAİL NACİ CANGÜL

Abstract:

In this thesis, Bernoulli numbers and polynomials are defined and several properties and usage areas are given.The thesis consists of four chapters. In the first chapter, the preliminary notions which are to be used in later chapters are given.In the second chapter Bernoulli numbers and polynomials are defined and relations to calculate them are considered. Also some properties of Bernoulli numbers and polynomials and the relations between these numbers and polynomials are given.In the third chapter some further properties of Bernoulli numbers and polynomials are given and some usage areas of them, relations with similar numbers, and series expansion of some functions by means of these numbers are studied.In the fourth and final chapter, generalised Bernoulli numbers and polynomials which are just some special cases of classical Bernoulli numbers and polynomials are defined and some properties are given.