New trigonometric identities and reciprocity laws of generalized Dedekind sums II
Genki Shibukawa
TL;DR
This paper introduces new trigonometric identities involving derivatives of cosecant and cotangent functions, leading to novel reciprocity laws for generalized Dedekind sums, expanding the mathematical understanding of these sums.
Contribution
It presents new product-to-sum formulas for derivatives of cosecant and cotangent, and derives new reciprocity laws for generalized Dedekind sums from these identities.
Findings
New trigonometric identities for derivatives of cosecant and cotangent
Reciprocity laws for generalized Dedekind sums derived from these identities
Enhanced understanding of the structure of Dedekind sums
Abstract
We obtain new trigonometric identities, which are product-to-sum type formulas for derivative of the cosecant and cotangent functions. Further, from specializations of our formulas, we derive new reciprocity laws of generalized Dedekind sums.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical Inequalities and Applications · Mathematical functions and polynomials