Analytic Continuation of q-Euler numbers and polynomials

2008/01/03 by T. Kim, Kim, T.
Mathematics · #11B68 #11S80 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B68 #msc:11S80

paper · pdf · doi:10.48550/arxiv.0801.0480

5 pages

arxiv created 2008/01/03 · openalex publication_date 2008/01/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ζ_E,q(s) in terms of nested series of ζ_E,q(n) is derived. Finally we introduce the new concept of the dynamics of analytically continued q-Euler numbers and polynomials.

Citations

• The p-adic generalized twisted (h,q)-euler-l-function and its applications

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