Apostol considered generalized Dedekind sums by replacing the first Bernoulli function appearing in Dedekind sums by any Bernoulli functions and derived a reciprocity relation for them. Recently, poly-Dedekind sums were introduced by replacing the first Bernoulli function appearing in Dedekind sums by any type 2 poly-Bernoulli functions of arbitrary indices and were shown to satisfy a reciprocity relation. In this paper, we consider other poly-Dedekind sums that are obtained by replacing the first Bernoulli function appearing in Dedekind sums by any poly-Bernoulli functions of arbitrary indices. We derive a reciprocity relation for these poly-Dedekind sums.

中文翻译：

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与poly-Bernoulli函数相关的Poly-Dedekind和

Apostol通过将出现在Dedekind和中的第一个Bernoulli函数替换为任何Bernoulli函数来考虑广义Dedekind和，并为其得出了对等关系。最近，通过用任意指数的任何类型2的poly-Bernoulli函数替换Dedekind求和中出现的第一个Bernoulli函数，引入了poly-Dedekind和，并证明它们满足互易关系。在本文中，我们考虑通过用任意指数的任何多元-伯努利函数代替Dedekind和中出现的第一个伯努利函数而获得的其他多元-Dedekind和。我们推导了这些多-Dedekind和的互惠关系。