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

Abstract EN

Using numerical investigation, we observe the behavior of complex roots of the Euler polynomials E n ( x ) .

By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the Euler polynomials E n ( x ) .

Finally, we show the Julia set of Newton iteration function R ( x ) = x - E n ( x ) / E n ′ ( x ) .