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Open AccessArticle

Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials

1
Faculty of Science, Kunming University of Science and Technology, Kunming 650500, Yunnan, China
2
Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, Gaziantep TR-27410, Turkey
3
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
4
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
5
Zewail City of Science andTechnology, University of Science and Technology, Cairo 82524, Egypt
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 329; https://doi.org/10.3390/math6120329
Received: 20 November 2018 / Revised: 6 December 2018 / Accepted: 10 December 2018 / Published: 14 December 2018
(This article belongs to the Special Issue Special Functions and Applications)
In this paper, we present a systematic and unified investigation for the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the Apostol-Genocchi polynomials. By applying the generating-function methods and summation-transform techniques, we establish some higher-order convolutions for the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the Apostol-Genocchi polynomials. Some results presented here are the corresponding extensions of several known formulas. View Full-Text
Keywords: Apostol-Bernoulli polynomials; Apostol-Euler polynomials; Apostol-Genocchi polynomials; convolution identities; stirling numbers of the first and second kind Apostol-Bernoulli polynomials; Apostol-Euler polynomials; Apostol-Genocchi polynomials; convolution identities; stirling numbers of the first and second kind
MDPI and ACS Style

He, Y.; Araci, S.; Srivastava, H.M.; Abdel-Aty, M. Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials. Mathematics 2018, 6, 329.

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