Fourier series of sums of products of ordered Bell and poly-Bernoulli functions

Taekyun Kim; Dae San Kim; Dmitry V Dolgy; Jin-Woo Park

doi:10.1186/s13660-017-1359-2

Fourier series of sums of products of ordered Bell and poly-Bernoulli functions

J Inequal Appl. 2017;2017(1):84. doi: 10.1186/s13660-017-1359-2. Epub 2017 Apr 28.

Authors

Taekyun Kim^{1

2}, Dae San Kim³, Dmitry V Dolgy⁴, Jin-Woo Park⁵

Affiliations

¹ Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin, 300160 China.
² Department of Mathematics, Kwangwoon University, Seoul, 139-701 Republic of Korea.
³ Department of Mathematics, Sogang University, Seoul, 121-742 Republic of Korea.
⁴ Hanrimwon, Kwangwoon University, Seoul, 139-701 Republic of Korea.
⁵ Department of Mathematics Education, Daegu University, Gyeongsan-si, Gyeongsangbuk-do 712-714 Republic of Korea.

Abstract

In this paper, we study three types of sums of products of ordered Bell and poly-Bernoulli functions and derive their Fourier series expansion. In addition, we express those functions in terms of Bernoulli functions.

Keywords: Fourier series; ordered Bell function; poly-Bernoulli function.