On The Generalized Euler Polynomials Of The Second Kind

Abstract

Many mathematicians have studied varies relations between Euler numbers En, Bernoulli numbers Bn and Genocchi numbers Gn. They have found numerous important applications in number theory. In this thesis we explain the term of Generalized Euler Polynoials of the Second kind. The generalized Euler polynomials are related to the Bernoulli numbers and polynomials, also Euler polynomials are related to Bernoulli numbers. In this thesis we de ne the Generalized Euler Polynomials of the Second Kinds ~"n(x): TheGeneralized Euler Polynomials of the Second Kind ~"n(x) are related to Genocchi numbers. In this thesis we also explain some properties of the generalized Euler polynomials them selves (the generalized Euler polynomials of the second kinds (~"n(x)) with Euler polynomials(En(x))). The Generalized Euler Polynomials of the Second Kinds ~"n(x) is used to induce the main result of this thesis