Preprint Article Version 1 This version not peer reviewed

Applications of q-Umbral Calculus to Modi…ed Apostol Type q-Bernoulli Polynomials

Version 1 : Received: 16 December 2017 / Approved: 18 December 2017 / Online: 18 December 2017 (10:01:24 CET)

How to cite: Acikgoz, M.; Ates, R.; Duran, U.; Araci, S. Applications of q-Umbral Calculus to Modi…ed Apostol Type q-Bernoulli Polynomials. Preprints 2017, 2017120118 (doi: 10.20944/preprints201712.0118.v1). Acikgoz, M.; Ates, R.; Duran, U.; Araci, S. Applications of q-Umbral Calculus to Modi…ed Apostol Type q-Bernoulli Polynomials. Preprints 2017, 2017120118 (doi: 10.20944/preprints201712.0118.v1).

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.

Subject Areas

q-umbral calculus; apostol-bernoulli polynomials; modi.ed apostol type q-bernoulli polynomials; q-appell polynomials; generating functions

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