Multifarious results for q-Hermite-based Frobenius-type Eulerian polynomials

Waseem Ahmad Khan, Idrees Ahmad Khan, Mehmet Acikgoz and Ugur Duran
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 2, Pages 127—141
DOI: 10.7546/nntdm.2020.26.2.127-141
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Authors and affiliations

Waseem Ahmad Khan
Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University
Al Khobar, 31952, Saudi Arabia

Idrees Ahmad Khan
Department of Mathematics, Integral University
Lucknow-226026, India

Mehmet Acikgoz
Department of Mathematics, University of Gaziantep
TR-27310 Gaziantep, Turkey

Ugur Duran
Department of the Basic Concepts of Engineering, Iskenderun Technical University
TR-31200 Hatay, Turkey


In this paper, a new class of q-Hermite-based Frobenius-type Eulerian polynomials is introduced by means of generating function and series representation. Several fundamental formulas and recurrence relations for these polynomials are derived via different generating methods. Furthermore, diverse correlations including the q-Apostol-Bernoulli polynomials, the q-Apostol-Euler poynoomials, the q-Apostol-Genocchi polynomials and the q-Stirling numbers of the second kind are also established by means of the their generating functions.


  • Hermite polynomials
  • Frobenius-type Eulerian polynomials
  • Hermite-based Frobenius-type Eulerian polynomials
  • q-numbers
  • q-polynomials

2010 Mathematics Subject Classification

  • 11B73
  • 11B83
  • 11B68


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Cite this paper

Khan, W. A., Khan, I. A., Acikgoz, M., & Duran, U. (2020). Multifarious results for q-Hermite-based Frobenius-type Eulerian polynomials. Notes on Number Theory and Discrete Mathematics, 26 (2), 127-141, doi: 10.7546/nntdm.2020.26.2.127-141.

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