q-Euler Numbers and Polynomials Associated with Basic Zeta Functions

2008/07/17 by Taekyun Kim, Kim, Taekyun
Mathematics · #11B68 #11S80 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #math.NT #msc:11B68 #msc:11S80

paper · pdf · doi:10.48550/arxiv.0807.2682

9 pages

arxiv created 2008/07/17 · openalex publication_date 2008/07/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give the q-extension of Euler numbers which can be viewed as interpolating of the q-analogue of Euler zeta function ay negative integers, in the same way that Riemann zeta function interpolates Bernoulli numbers at negative integers. Finally we woll treat some identities of the q-extension of the euler numbers by using fermionic p-adic q-integration on Z_p.

Citations

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

Related

• A New approach to q-zeta function
• q-Euler numbers and polynomials associated with multiple q-zeta functions
• Note on q-extensions of Euler numbers and polynomials of higher order
• On the q-Extensions of the Bernoulli and Euler Numbers, Related Identities and Lerch Zeta Function
• A note on p-adic q-integrals associated with q-Euler numbers