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.
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Keywords:
Apostol-Bernoulli polynomials; Apostol-Euler polynomials; Apostol-Genocchi polynomials; convolution identities; stirling numbers of the first and second kind
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
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. https://doi.org/10.3390/math6120329
AMA Style
He Y, Araci S, Srivastava HM, Abdel-Aty M. Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials. Mathematics. 2018; 6(12):329. https://doi.org/10.3390/math6120329
Chicago/Turabian StyleHe, Yuan; Araci, Serkan; Srivastava, Hari M.; Abdel-Aty, Mahmoud. 2018. "Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials" Mathematics 6, no. 12: 329. https://doi.org/10.3390/math6120329
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