Reciprocity of poly-Dedekind-type DC sums involving poly-Euler functions

Advances in Difference Equations

article

Ma, Yuankui¹  Kim, Dae San²  Lee, Hyunseok³  Kim, Hanyoung³  Kim, Taekyun¹ 

[1] School of Science, Xi’an Technological University;Department of Mathematics, Sogang University;Department of Mathematics, Kwangwoon University

关键词: Poly-Dedekind type DC sums;    Poly-Genocchi polynomials;    Poly-Euler polynomials;    Poly-Euler functions;   

DOI  :  10.1186/s13662-020-03194-8

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. The Dedekind sums and their generalizations are defined in terms of Bernoulli functions and their generalizations, and are shown to satisfy some reciprocity relations. In contrast, Dedekind-type DC (Daehee and Changhee) sums and their generalizations are defined in terms of Euler functions and their generalizations. The purpose of this paper is to introduce the poly-Dedekind-type DC sums, which are obtained from the Dedekind-type DC sums by replacing the Euler function by poly-Euler functions of arbitrary indices, and to show that those sums satisfy, among other things, a reciprocity relation.

【 授权许可】

CC BY