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.

在来自模块组的替换下，经典Dedekind和出现在Dedekind eta函数对数的变换行为中。用伯努利函数及其广义来定义Dedekind和及其一般化，并证明它们满足某些互惠关系。相反，Dedekind型DC（Daehee和Changhee）的总和及其泛化是根据Euler函数及其泛化来定义的。本文的目的是介绍由Dedekind型DC和获得的poly-Dedekind型DC和，用任意指数的Poly-Euler函数代替Euler函数，并证明这些和满足其他的，互惠的关系。