Explicit identities involving truncated exponential polynomials and phenomenon of scattering of their zeros

Abstract

In this paper, we study differential equations arising from the generating functions of truncated exponential polynomials. We give explicit identities for the truncated polynomials. Using numerical investigation, we observe the behavior of complex roots of the truncated polynomials en(x). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the truncated polynomials en(x).