Identities involving q-Genocchi numbers and polynomials

Serkan Araci, Mehmet Acikgoz, Hassan Jolany and Yuan He
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 20, 2014, Number 5, Pages 64–74
Full paper (PDF, 189 Kb)

Details

Authors and affiliations

Serkan Araci
Department of Economics
Faculty of Economics, Administrative and Social Sciences
Hasan Kalyoncu University
TR-27410 Gaziantep, Turkey

Mehmet Acikgoz
Department of Mathematics
University of Gaziantep, Faculty of Science and Arts
27310 Gaziantep, Turkey

Hassan Jolany
School of Mathematics, Statistics and Computer Science
University of Tehran, Iran

Yuan He
Department of Mathematics
Kunming University of Science and Technology
Kunming, Yuannan 650500, People’s Republic of China

Abstract

In this paper, we focus on the q-Genocchi numbers and polynomials. We introduce new identities of the q-Genocchi numbers and polynomials by using the fermionic p-adic integral on ℤ_p. Also, we give Cauchy-integral formula for the q-Genocchi polynomials and derive the distribution formula q-Genocchi polynomials by using measure theory on p-adic integral. Finally, we get q-Zeta-type function by using Mellin transformation (sometimes known as Laplace transformation) and show that this function interpolates to the q-Genocchi polynomials at negative integers.

Keywords

• Genocchi numbers and polynomials
• q-Genocchi numbers and polynomials
• p-adic q-integral on ℤ_p
• Mellin transformation
• q-Zeta function

AMS Classification

• Primary: 05A10, 11B65
• Secondary: 11B68, 11B73

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