# A NOTE ON THE q-EULER NUMBERS AND POLYNOMIALS WITH WEIGHT (α,ω)

• Rim, Seog-Hoon (Department of Mathematics Education, Kyungpook National University) ;
• Jeong, Joo-Hee (Department of Mathematics Education, Kyungpook National University)
• Accepted : 2012.03.27
• Published : 2012.06.25

#### Abstract

The main purpose of this paper is to introduce a new type of $q$-Euler numbers and polynomials with weak weight (${\alpha}$,${\omega}$): $\tilde{E}^{({\alpha},{\omega})}_{n,q}$ and $\tilde{E}^{({\alpha},{\omega})}_{n,q}(x)$, respectively. By using the fermionic $p$-adic $q$-integral on $\mathbb{Z}_p$, we can obtain some results and derive some recurrence identities for the $q$-Euler numbers and polynomials with weak weight (${\alpha}$,${\omega}$).

#### Acknowledgement

Supported by : Kyungpook National University

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