Dynamics of the Zeros of Analytic Continued (h,q)-Euler Polynomials

Abstract

In this paper, we study that the $(h,q)$-Euler numbers $E_{n,q}^{(h)}$ and $(h,q)$-Euler polynomials $E_{n,q}^{(h)}(x)$ are analytic continued to $E_q^{(h)}(s)$ and $E_q^{(h)}(s,w)$. We investigate the new concept of dynamics of the zeros of analytic continued polynomials related to solution of Bernoulli equation. Finally, we observe an interesting phenomenon of “scattering” of the zeros of $E_q^{(h)}(s,w)$.