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

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## 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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## Related papers

## Cite this paper

APAAraci, S, M. Acikgoz, H. Jolany, & Y. He. (2014). Identities involving *q*-Genocchi numbers and polynomials. Notes on Number Theory and Discrete Mathematics, 20(5), 64-74.

Araci, Serkan, Mehmet Acikgoz, Hassan Jolany, and Yuan He. “Identities Involving *q*-Genocchi Numbers and Polynomials.” Notes on Number Theory and Discrete Mathematics 20, no. 5 (2014): 64-74.

Araci, Serkan, Mehmet Acikgoz, Hassan Jolany, and Yuan He. “Identities Involving *q*-Genocchi Numbers and Polynomials.” Notes on Number Theory and Discrete Mathematics 20.5 (2014): 64-74. Print.