Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials
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Faculty of Science, Kunming University of Science and Technology, Kunming 650500, Yunnan, China
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Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, Gaziantep TR-27410, Turkey
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Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
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Department of Medical Research, China Medical University, Taichung 40402, Taiwan
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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
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Revised: 6 December 2018
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Accepted: 10 December 2018
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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
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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, Serkan Araci, Hari M. Srivastava, and Mahmoud Abdel-Aty. 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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