## Abstract and Applied Analysis

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

C. S. Ryoo

#### 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 ${E}_{q}^{(h)}(s,w)$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 537864, 9 pages.

Dates
First available in Project Euclid: 27 February 2015

https://projecteuclid.org/euclid.aaa/1425049865

Digital Object Identifier
doi:10.1155/2014/537864

Mathematical Reviews number (MathSciNet)
MR3280866

Zentralblatt MATH identifier
07022576

#### Citation

Ryoo, C. S. Dynamics of the Zeros of Analytic Continued $(h,q)$ -Euler Polynomials. Abstr. Appl. Anal. 2014 (2014), Article ID 537864, 9 pages. doi:10.1155/2014/537864. https://projecteuclid.org/euclid.aaa/1425049865