Acikgoz, M.; Ates, R.; Duran, U.; Araci, S. Applications of q-Umbral Calculus to Modified Apostol Type q-Bernoulli Polynomials. Journal of Mathematics and Statistics 2018, 14, 7-15.
Acikgoz, M.; Ates, R.; Duran, U.; Araci, S. Applications of q-Umbral Calculus to Modified Apostol Type q-Bernoulli Polynomials. Journal of Mathematics and Statistics 2018, 14, 7-15.
Acikgoz, M.; Ates, R.; Duran, U.; Araci, S. Applications of q-Umbral Calculus to Modified Apostol Type q-Bernoulli Polynomials. Journal of Mathematics and Statistics 2018, 14, 7-15.
Acikgoz, M.; Ates, R.; Duran, U.; Araci, S. Applications of q-Umbral Calculus to Modified Apostol Type q-Bernoulli Polynomials. Journal of Mathematics and Statistics 2018, 14, 7-15.
Abstract
This article aims to identify the generating function of modi ed Apostol type q-Bernoulli polynomials. With the aid of this generating function, some properties of modi ed 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 modi ed q-Bernoulli polynomials as a linear combination of some known polynomials which we stated in the paper.
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.