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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

Applications of q-Umbral Calculus to Modified Apostol Type q-Bernoulli Polynomials

Mehmet Acikgoz1, Resul Ates1, Ugur Duran1 and Serkan Araci2
  • 1 University of Gaziantep, Turkey
  • 2 Hasan Kalyoncu University, Turkey

Abstract

This article aims to identify the generating function of modified Apostol type q-Bernoulli polynomials. With the aid of this generating function, some properties of modified Apostol type q-Bernoulli polynomials are given. It is shown that aforementioned polynomials are q-Appell. Hence, we make use of these polynomials to have applications on q-Umbral calculus. From those applications, we derive some theorems in order to get Apostol type modified q-Bernoulli polynomials as a linear combination of some known polynomials which we stated in the paper.

Journal of Mathematics and Statistics
Volume 14 No. 1, 2018, 7-15

DOI: https://doi.org/10.3844/jmssp.2018.7.15

Submitted On: 18 November 2017 Published On: 4 January 2018

How to Cite: Acikgoz, M., Ates, R., Duran, U. & Araci, S. (2018). Applications of q-Umbral Calculus to Modified Apostol Type q-Bernoulli Polynomials. Journal of Mathematics and Statistics, 14(1), 7-15. https://doi.org/10.3844/jmssp.2018.7.15

Open AccessCopyright: © 2018 Mehmet Acikgoz, Resul Ates, Ugur Duran and Serkan Araci. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • q-Umbral Calculus
  • Apostol-Bernoulli Polynomials
  • Modified Apostol Type q-Bernoulli Polynomials
  • q-Appell Polynomials
  • Generating Functions