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Abstract and Applied Analysis
Volume 2018, Article ID 2937950, 13 pages
https://doi.org/10.1155/2018/2937950
Research Article

An Extended Generalized -Extensions for the Apostol Type Polynomials

1Universidad del Atlántico, Barranquilla, Colombia
2GICBAS, Universidad de la Costa, Barranquilla, Colombia
3Programa de Matemática, Universidad del Atlántico, Km 7, Vía Pto. Colombia, Barranquilla, Colombia

Correspondence should be addressed to Alejandro Urieles; oc.ude.ocitnaltainu.liam@seleiruordnajela

Received 5 February 2018; Revised 3 May 2018; Accepted 22 May 2018; Published 2 July 2018

Academic Editor: Allan Peterson

Copyright © 2018 Letelier Castilla et al. 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.

Abstract

Through a modification on the parameters associated with generating function of the -extensions for the Apostol type polynomials of order and level , we obtain some new results related to a unified presentation of the -analog of the generalized Apostol type polynomials of order and level . In addition, we introduce some algebraic and differential properties for the -analog of the generalized Apostol type polynomials of order and level and the relation of these with the -Stirling numbers of the second kind, the generalized -Bernoulli polynomials of level , the generalized -Apostol type Bernoulli polynomials, the generalized -Apostol type Euler polynomials, the generalized -Apostol type Genocchi polynomials of order and level , and the -Bernstein polynomials.