Geodesic
Fourier series of sums of products of $r$-derangement functions
Kim, Taekyun 1 ; Kim, Dae San 2 ; Kwon, Huck-In 1 ; Jang, Lee-Chae 3
1 Department of Mathematics, Kwangwoon University, Seoul 139-701, S. Korea
2 Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
3 Graduate School of Education, Konkuk University, Seoul 143-701, Republic of Korea
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 4, p. 575-590.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.011.04.12
Classification : 11B83, 11B68, 42A16
Keywords: Fourier series, \(r\)-derangement polynomials, Bernoulli polynomials

Kim, Taekyun  1 ; Kim, Dae San  2 ; Kwon, Huck-In  1 ; Jang, Lee-Chae  3

1 Department of Mathematics, Kwangwoon University, Seoul 139-701, S. Korea
2 Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
3 Graduate School of Education, Konkuk University, Seoul 143-701, Republic of Korea 
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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 its applications, Tome 11 (2018) no. 4, p. 575-590. doi : 10.22436/jnsa.011.04.12. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.04.12/

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