Applications of q-Umbral Calculus to Modified Apostol Type q-Bernoulli Polynomials
- 1 University of Gaziantep, Turkey
- 2 Hasan Kalyoncu University, Turkey
Published On: 4 January 2018
Copyright: © 2020 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.
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.
- q-Umbral Calculus
- Apostol-Bernoulli Polynomials
- Modified Apostol Type q-Bernoulli Polynomials
- q-Appell Polynomials
- Generating Functions