Taekyun Kim - Department of Mathematics, Kwangwoon University, Seoul 139-701, S. Korea. Dae San Kim - Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea. Huck-In Kwon - Department of Mathematics, Kwangwoon University, Seoul 139-701, S. Korea. Lee-Chae Jang - Graduate School of Education, Konkuk University, Seoul 143-701, Republic of Korea.
A derangement is a permutation that has no fixed point and the derangement number \(d_m\) is the number of fixed point-free permutations on an \(m\) element set. A generalization of the derangement numbers are the \(r\)-derangement numbers and their natural companions are the \(r\)-derangement polynomials. In this paper we will study three types of sums of products of \(r\)-derangement functions and find Fourier series expansions of them. In addition, we will express them in terms of Bernoulli functions. As immediate corollaries to this, we will be able to express the corresponding three types of polynomials as linear combinations of Bernoulli polynomials.
Taekyun Kim, Dae San Kim, Huck-In Kwon, Lee-Chae Jang, Fourier series of sums of products of \(r\)-derangement functions, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 4, 575--590
Kim Taekyun, Kim Dae San, Kwon Huck-In, Jang Lee-Chae, Fourier series of sums of products of \(r\)-derangement functions. J. Nonlinear Sci. Appl. (2018); 11(4):575--590
Kim, Taekyun, Kim, Dae San, Kwon, Huck-In, Jang, Lee-Chae. "Fourier series of sums of products of \(r\)-derangement functions." Journal of Nonlinear Sciences and Applications, 11, no. 4 (2018): 575--590
