A Numerical Investigation on the Structure of the Zeros of Euler Polynomials

Abstract

Using numerical investigation, we observe the behavior of complex roots of the Euler polynomialsEn(x). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the Euler polynomialsEn(x). Finally, we show the Julia set of Newton iteration functionR(x)=x-En(x)/En′(x).