Note on q-extensions of Euler numbers and polynomials of higher order

2007/10/31 by Taekyun Kim, Kim, Taekyun, Lee-Chae Jang +4
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.0710.5810

11 pages

arxiv created 2007/10/31 · openalex publication_date 2007/10/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted (h,q)-extension of Euler polynomials and numbers, by using p-adic q-deformed fermionic integral on \Bbb Z_p. By applying their generating functions, they derived the complete sums of products of the twisted (h,q)-extension of Euler polynomials and numbers, see[13, 14]. In this paper we cosider the new q-extension of Euler numbers and polynomials to be different which is treated by Ozden-Simsek-Cangul. From our q-Euler numbers and polynomials we derive some interesting identities and we construct q-Euler zeta functions which interpolate the new q-Euler numbers and polynomials at a negative integer. Furthermore we study Barnes' type q-Euler zeta functions. Finally we will derive the new formula for " sums products of q-Euler numbers and polynomials" by using fermionic p-adic q-integral on \Bbb Z_p.

Citations

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

Related

• q-Euler Numbers and Polynomials Associated with Basic Zeta Functions
• Some new identities on the twisted (h, q)- Euler numbers and q-Bernstein polynomials
• The fermionic p-adic integrals on Zp associated with extended q-Euler numbers and polynomials
• q-Volkenborn Integration and Its Applications
• On the q-Extensions of the Bernoulli and Euler Numbers, Related Identities and Lerch Zeta Function