Waseem A. Khan and Divesh Srivastava

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 26, 2020, Number 1, Pages 75—85

DOI: 10.7546/nntdm.2020.26.1.75-85

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## Details

### Authors and affiliations

Waseem A. Khan

*Department of Mathematics and Natural Sciences
Prince Mohammad Bin Fahd University
P.O Box 1664, Al Khobar 31952, Saudi Arabia
*

Divesh Srivastava

*Department of Mathematics, Faculty of Science
Integral University
Lucknow-226026, India*

### Abstract

The present article is to introduce a new class of *q*-Hermite based Apostol-type

polynomials and to investigate their properties and characteristics. In particular, the generating functions, series expression and explicit and recurrence relations for these polynomials are established. We derive some relationships for *q*-Hermite based Apostol-type polynomials associated with *q*-Apostol-type Bernoulli polynomials, *q*-Apostol-type Euler and *q*-Apostol-type Genocchi polynomials.

### Keywords

*q*-polynomials*q*-Hermite-based Apostol-type polynomials*q*-recurrence relations

### 2010 Mathematics Subject Classification

- 05A10
- 05A15
- 11B68
- 16B65
- 33C45

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## Related papers

- Goubi, M. (2020). Explicit formula of a new class of
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## Cite this paper

Khan, W. A. & Srivastava D. (2020). A new class of q-Hermite-based Apostol-typepolynomials and its applications. Notes on Number Theory and Discrete Mathematics, 26(1), 75-85, doi: 10.7546/nntdm.2020.26.1.75-85.