Journal of Mathematics and Statistics

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

Mehmet Acikgoz, Resul Ates, Ugur Duran and Serkan Araci

Journal of Mathematics and Statistics

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.

Copyright

© 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.