Analytic continuation of q-Euler numbers and polynomials

Abstract

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