Analytic continuation of q-Euler numbers and polynomials

In this work we study the qq-Euler numbers and polynomials analytically continued to Eq(s)Eq(s). A new formula for Euler’s qq-zeta function ζE,q(s)ζE,q(s) in terms of nested series of ζE,q(n)ζE,q(n) is derived. Finally we introduce the new concept of dynamics of the zeros of analytically continued qq-Euler polynomials.