Advances in Difference Equations | |
Identities on poly-Dedekind sums | |
Taekyun Kim1  Hyunseok Lee1  Dae San Kim2  Lee-Chae Jang3  | |
[1] Department of Mathematics, Kwangwoon University, 139-701, Seoul, Republic of Korea;Department of Mathematics, Sogang University, 121-742, Seoul, Republic of Korea;Graduate School of Education, Konkuk University, Seoul, Republic of Korea; | |
关键词: Poly-Dedekind sum; Polyexponential function; Type 2 poly-Bernoulli polynomial; 11F20; 11B68; 11B83; | |
DOI : 10.1186/s13662-020-03024-x | |
来源: Springer | |
【 摘 要 】
Dedekind sums occur in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. In 1892, Dedekind showed a reciprocity relation for the Dedekind sums. Apostol generalized Dedekind sums by replacing the first Bernoulli function appearing in them by any Bernoulli functions and derived a reciprocity relation for the generalized Dedekind sums. In this paper, we consider the poly-Dedekind sums obtained from the Dedekind sums by replacing the first Bernoulli function by any type 2 poly-Bernoulli functions of arbitrary indices and prove a reciprocity relation for the poly-Dedekind sums.
【 授权许可】
CC BY
【 预 览 】
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