## Journal of Applied Mathematics

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

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

H. Y. Lee, N. S. Jung, and C. S. Ryoo

#### Abstract

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

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1331818668

**Digital Object Identifier**

doi:10.1155/2011/497409

**Mathematical Reviews number (MathSciNet)**

MR2852850

#### Citation

Lee, H. Y.; Jung, N. S.; Ryoo, C. S. A Note on the q -Euler Numbers and Polynomials with Weak Weight α. J. Appl. Math. 2011 (2011), Article ID 497409, 14 pages. doi:10.1155/2011/497409. https://projecteuclid.org/euclid.jam/1331818668