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

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