scholarly journals Fourier series of higher-order Bernoulli functions and their applications

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Seog-Hoon Rim ◽  
Dmitry V. Dolgy
Keyword(s):  
Fourier Series ◽  
Higher Order ◽  
Bernoulli Functions

scholarly journals Fourier series of functions involving higher-order ordered Bell polynomials

2017 ◽  
Vol 15 (1) ◽  
pp. 1606-1617 ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Gwan-Woo Jang ◽  
Lee Chae Jang
Keyword(s):  
Number Theory ◽  
Fourier Series ◽  
Higher Order ◽  
Series Expansions ◽  
Bell Polynomials ◽  
Bell Numbers ◽  
Enumerative Combinatorics ◽  
Bernoulli Functions ◽  
Series Of Functions

AbstractIn 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.

scholarly journals Fourier series of sums of products of poly-Bernoulli functions and their applications

2017 ◽  
Vol 10 (05) ◽  
pp. 2384-2401 ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Dmitry V. Dolgy ◽  
Jin-Woo Park
Keyword(s):  
Fourier Series ◽  
Bernoulli Functions ◽  
Sums Of Products

scholarly journals Series of sums of products of higher-order Bernoulli functions

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Gwan-Woo Jang ◽  
Jongkyum Kwon
Keyword(s):  
Higher Order ◽  
Bernoulli Functions ◽  
Sums Of Products

scholarly journals Fourier series of functions associated with higher-order Bernoulli polynomials

2017 ◽  
Vol 10 (05) ◽  
pp. 2579-2591
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Dmitry V. Dolgy ◽  
Jin-Woo Park
Keyword(s):  
Fourier Series ◽  
Bernoulli Polynomials ◽  
Higher Order ◽  
Series Of Functions

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

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Dmitry V Dolgy ◽  
Jin-Woo Park
Keyword(s):  
Fourier Series ◽  
Bernoulli Functions ◽  
Sums Of Products
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