Fourier expansions for Genocchi polynomials of higher order

Volume 22, Issue 1, pp 59--72 http://dx.doi.org/10.22436/10.22436/jmcs.022.01.06

Publication Date: July 05, 2020 Submission Date: April 01, 2020 Revision Date: May 11, 2020 Accteptance Date: May 16, 2020

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Authors

Cristina B. Corcino - Research Institute for Computational Mathematics and Physics, Cebu Normal University, Osmena Boulevard, Cebu City, Philippines. Baby Ann A. Damgo - Mathematics Department, Cebu Normal University, Osmena Boulevard, Cebu City, Philippines. Roberto B. Corcino - Research Institute for Computational Mathematics and Physics, Cebu Normal University, Osmena Boulevard, Cebu City, Philippines.

Abstract

In this paper, Fourier expansions and integral representations for Genocchi polynomials of higher order are established. Using the Fourier expansion, the explicit formula for Genocchi polynomials at rational arguments in terms of Hurwitz zeta function is also obtained.

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Keywords

• Genocchi polynomials
• Bernoulli polynomials
• Euler polynomials
• Fourier series
• Hurwitz zeta function

MSC

•  11B68
•  42A16
•  11M35

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