An Elementary Derivation of Finite Cotangent Sums

DOI10.1080/00029890.2022.2094171zbMath1499.11256OpenAlexW4285495178MaRDI QIDQ5103248

Bryan Park

Publication date: 23 September 2022

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00029890.2022.2094171

zbMATH Keywords

cotangent sumsLaurent coefficients

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Trigonometric and exponential sums (general theory) (11L03)

Cites Work

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• Exact evaluations of finite trigonometric sums by sampling theorems
• Summation formulae for finite cotangent sums
• Partial fractions and trigonometric identities
• Generating functions and generalized Dedekind sums.
• Explicit evaluations and reciprocity theorems for finite trigonometric sums
• The trace method for cotangent sums
• Explicit expressions for finite trigonometric sums
• Some polynomials associated with Williams' limit formula for $\zeta (2n)$
• A Simple Proof of the Formula ∑ ∞ k = 1 = π 2 /6
• Another Elementary Proof of Euler's Formula for ζ(2n)

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