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
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

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.

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Keywords

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