Journal of Applied Mathematics
Volume 2011 (2011), Article ID 497409, 14 pages
Research Article

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

Department of Mathematics, Hannam University, Daejeon 306-791, Republic of Korea

Received 4 June 2011; Accepted 30 August 2011

Academic Editor: Mohamad Alwash

Copyright © 2011 H. Y. Lee et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We construct a new type of 𝑞 -Euler numbers and polynomials with weak weight 𝛼 : 𝐸 ( 𝛼 ) 𝑛 , 𝑞 , 𝐸 ( 𝛼 ) 𝑛 , 𝑞 ( 𝑥 ) , respectively. Some interesting results and relationships are obtained. Also, we observe the behavior of roots of the 𝑞 -Euler numbers 𝐸 ( 𝛼 ) 𝑛 , 𝑞 and polynomials 𝐸 ( 𝛼 ) 𝑛 , 𝑞 ( 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 ( 𝛼 ) 𝑛 , 𝑞 with weak weight 𝛼 .