In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the preferred arrangement numbers). In this paper, we study Fourier series of functions related to higher-order ordered Bell polynomials and derive their Fourier series expansions. In addition, we express each of them in terms of Bernoulli functions.
@article{bwmeta1.element.doi-10_1515_math-2017-0134,
author = {Taekyun Kim and Dae San Kim and Gwan-Woo Jang and Lee Chae Jang},
title = {Fourier series of functions involving higher-order ordered Bell polynomials},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {1606-1617},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0134}
}
Taekyun Kim; Dae San Kim; Gwan-Woo Jang; Lee Chae Jang. Fourier series of functions involving higher-order ordered Bell polynomials. Open Mathematics, Tome 15 (2017) pp. 1606-1617. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0134/