Fourier series of sums of products of Bernoulli and Euler/Genocchi functions

Taekyun Kim, Dae San Kim, Toufik Mansour and Gwan-Woo Jang
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 1, Pages 76–93
DOI: 10.7546/nntdm.2018.24.1.76-93
Full paper (PDF, 282 Kb)

Details

Authors and affiliations

Taekyun Kim
Department of Mathematics, College of Science, Tianjin Polytechnic University
Tianjin 300160, China, and
Department of Mathematics, Kwangwoon University
Seoul 139-701, South Korea

Dae San Kim
Department of Mathematics, Sogang University
Seoul 121-742, South Korea

Toufik Mansour
Department of Mathematics, University of Haifa
3498838 Haifa, Israel

Gwan-Woo Jang
Department of Mathematics, Kwangwoon University
Seoul 139-701, South Korea

Abstract

We study the Fourier series of functions related to sum of products of Bernoulli polynomials and either Euler or Genocchi polynomials. As consequences, several new identities for the Bernoulli, Euler, and Genocchi functions and numbers are derived.

Keywords

• Fourier series
• Bernoulli polynomials
• Euler polynomials
• Genocchi polynomials

2010 Mathematics Subject Classification

• 11B68
• 42A16

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