Summation formulae for finite cotangent sums

DOI10.1016/J.AMC.2009.06.053zbMath1220.11095OpenAlexW2007441166MaRDI QIDQ734874

Djurdje Cvijović

Publication date: 14 October 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.06.053

zbMATH Keywords

Bernoulli numberscontour integrationBernoulli polynomialscotangent sumstrigonometric sumsCauchy residue theoremfinite summationhigher order Bernoulli polynomialsalternate cotangent sums

Mathematics Subject Classification ID

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

Related Items (9)

An Elementary Derivation of Finite Cotangent Sums ⋮ Existence and stability of symmetric and asymmetric patterns for the half-Laplacian Gierer–Meinhardt system in one-dimensional domain ⋮ Summation formulae for finite tangent and secant sums ⋮ Dedekind and Hardy Type Sums and Trigonometric Sums Induced by Quadrature Formulas ⋮ Reciprocal relations for trigonometric sums ⋮ General order Euler sums with multiple argument ⋮ The trace method for cotangent sums ⋮ Two general families of integer-valued polynomials associated with finite trigonometric sums ⋮ Trigonometric sums by Hermite interpolations

Cites Work

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• Partial fractions and trigonometric identities
• Summations on trigonometric functions
• Explicit evaluations and reciprocity theorems for finite trigonometric sums
• Weighted trigonometric sums over a half-period
• Summation of a family of finite secant sums
• New trigonometric sums by sampling theorem
• Closed-form summation of two families of finite tangent sums
• Summation formulae on trigonometric functions
• Closed-form summation of the Dowker and related sums
• Some polynomials associated with Williams' limit formula for $\zeta (2n)$

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