## Journal of Applied Mathematics

### A Note on the $q$-Euler Numbers and Polynomials with Weak Weight $α$

#### Abstract

We construct a new type of q-Euler numbers and polynomials with weak weight $\alpha:{E}_{n,q}^{(\alpha )}$, ${E}_{n,q}^{(\alpha )}(x)$, respectively. Some interesting results and relationships are obtained. Also, we observe the behavior of roots of the q-Euler numbers ${E}_{n,q}^{(\alpha )}$ and polynomials ${E}_{n,q}^{(\alpha )}(x)$ with weak weight α. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of q-Euler polynomials ${E}_{n,q}^{(\alpha )}$ with weak weight α.

#### Article information

Source
J. Appl. Math., Volume 2011 (2011), Article ID 497409, 14 pages.

Dates
First available in Project Euclid: 15 March 2012