Bernoulli and euler polynomials

ABSTRACT: This thesis provides an overview of Bernoulli and Euler numbers. It describes the Bernoulli and Euler polynomials and investigates the relationship between the classes of the two polynomials. It also discusses some important identities using the _nite di_erence calculus and di_erentiation. The last part of this study is concerned with the Generalized Bernoulli and Euler polynomials. Furthermore, the properties obtained in the second chapter are also examined for the generalized Bernoulli and Euler polynomials in this part of the thesis. The Complementary Argument Theorem, the generating functions, the Multiplication and the Euler-Maclauren Theorems are widely used in obtaining the mentioned results. Keywords: Bernoulli -Euler Polynomials, Generalized Bernoulli -Euler Polynomials, Finite Difference. …………………………………………………………………………………………………………………………………………………………………………………………………………