A study on a type of degenerate poly-Dedekind sums

Abstract

Dedekind sums and their generalizations are defined in terms of Bernoulli functions and their generalizations. As a new generalization of the Dedekind sums, the degenerate poly-Dedekind sums, which are obtained from the Dedekind sums by replacing Bernoulli functions by degenerate poly-Bernoulli functions of arbitrary indices are introduced in this article and are shown to satisfy a reciprocity relation.

Keywords

• degenerate poly-dedekind sums
• degenerate polylogarithm functions
• degenerate poly-bernoulli polynomials
• 11f20
• 11b68
• 11b83