A Numerical Investigation on the Structure of the Zeros of Euler Polynomials. (31st May 2015)

• Record Type: Journal Article
• Authors: Ryoo, C. S.; Kang, J. Y.
• Other Names: Zhang Guang Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2015(2015)
• Publication Date: 2015-05-31
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2015/174173
• Languages: English
• ISSNs: 1026-0226

Abstract

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