Analytic Continuation of q-Euler numbers and polynomials

Details Analytic Continuation of q-Euler numbers and polynomials Analytic Continuation of q-Euler numbers and polynomials

2008-01-03

arxiv.org/abs/0801.0480v1

Mathematics

Number Theory

5 pages

Scientific paper

In this paper we study that the $q$-Euler numbers and polynomials are
analytically continued to $E_q(s)$. A new formula for the Euler's $q$-Zeta
function $\zeta_{E,q}(s)$ in terms of nested series of $\zeta_{E,q}(n)$ is
derived. Finally we introduce the new concept of the dynamics of analytically
continued $q$-Euler numbers and polynomials.

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