**Ugur Duran, Mehmet Acikgoz and Serkan Araci**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 25, 2019, Number 3, Pages 72-86

DOI: 10.7546/nntdm.2019.25.3.72-86

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## Details

### Authors and affiliations

Ugur Duran

*Department of the Basic Concepts of Engineering
Faculty of Engineering and Natural Sciences
Iskenderun Technical University
TR-31200 Hatay, Turkey
*

Mehmet Acikgoz

*Department of Mathematics
Faculty of Arts and Sciences
Gaziantep University
TR-27310 Gaziantep, Turkey
*

Serkan Araci

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

### Abstract

Motivated by Kurt’s blending generating functions of *q*-Apostol polynomials [16], we investigate some new identities and relations. We also aim to derive several new connections between these polynomials and generalized *q*-Stirling numbers of the second kind. Additionally, by making use of the fermionic *p*-adic integral over the *p*-adic numbers field, some relationships including unified Apostol-type *q*-polynomials and classical Euler numbers are obtained.

### Keywords

*q*-calculus- Apostol–Bernoulli polynomials
- Apostol–Euler polynomials
- Apostol–Genocchi polynomials
- Stirling numbers of second kind
- Fermionic
*p*-adic integral *p*-adic numbers

### 2010 Mathematics Subject Classification

- 05A30
- 11B68
- 11B73

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## Cite this paper

Duran, Ugur, Acikgoz, Mehmet & Araci , Serkan (2019). On applications of blending generating functions of *q*-Apostol-type polynomials. *Notes on Number Theory and Discrete Mathematics*, 25(3), 72-86, doi: 10.7546/nntdm.2019.25.3.72-86.