Analytic Continuation of q-Euler numbers and polynomials

T. Kim

Analytic Continuation of q-Euler numbers and polynomials

Number Theory 2008-01-04 v1

Authors: T. Kim

Abstract

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.

Keywords

q-series and q-analogues eulerian polynomials and bernoulli numbers zeta values and euler sums

Cite

@article{arxiv.0801.0480,
  title  = {Analytic Continuation of q-Euler numbers and polynomials},
  author = {T. Kim},
  journal= {arXiv preprint arXiv:0801.0480},
  year   = {2008}
}

Comments

5 pages

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