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 : e n,q (α),e n,q (α)(x),respectively. some interesting results and relationships are obtained. also,we observe the behavior of roots of the q-euler numbers e n,q (α) and polynomials e n,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 e n,q (α) with weak weight α. copyright © 2011 h. y. lee et al.