Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis

Volume 9, Issue 5, pp 2697--2704 http://dx.doi.org/10.22436/jnsa.009.05.66

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Authors

Armen Bagdasaryan - Department of Mathematics and Statistics, American University of the Middle East, Kuwait City, 15453 Egaila, Kuwait. - Institute for Control Sciences, Russian Academy of Sciences, 65 Profsoyuznaya, 117997 Moscow, Russia. Serkan Araci - Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, TR-27410 Gaziantep, Turkey. Mehmet Acikgoz - Department of Mathematics, Faculty of Arts and Sciences, University of Gaziantep, TR-27310 Gaziantep, Turkey. Yuan He - Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan 650500, People's Republic of China.

Abstract

In the present paper, we introduce a method in order to obtain some new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived from Bernoulli polynomial basis. Finally, by utilizing this method, we also get formulas for the convolutions of Bernoulli and Euler polynomials in terms of Apostol-Bernoulli polynomials of higher order.

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Keywords

• Generating function
• Bernoulli polynomials of higher order
• Euler polynomials of higher order
• Hermite polynomials
• Apostol-Bernoulli polynomials of higher order
• Apostol-Euler polynomials of higher order
• identities.

MSC

•  11B68
•  11S80

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