Poly-Dedekind sums associated with poly-Bernoulli functions
AbstractApostol 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.
2000 ◽
Vol 248
(6)
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pp. 492-500
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2017 ◽
Vol 201
(7-9)
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pp. 1209-1225
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2015 ◽
Vol 199
(7)
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pp. 1211-1213
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