Summation formulae for finite tangent and secant sums

DOI10.1016/J.AMC.2011.01.079zbMath1248.33004OpenAlexW2026255193MaRDI QIDQ648178

Djurdje Cvijović

Publication date: 22 November 2011

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

Full work available at URL: https://doi.org/10.1016/j.amc.2011.01.079

zbMATH Keywords

contour integrationBernoulli polynomialstrigonometric sumsEuler polynomialsCauchy residue theoremfinite summationhigher order Bernoulli polynomialssecant sumstangent sums

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Exponential and trigonometric functions (33B10)

Related Items (3)

Human and automated approaches for finite trigonometric sums ⋮ Dedekind and Hardy Type Sums and Trigonometric Sums Induced by Quadrature Formulas ⋮ Trigonometric sums by Hermite interpolations

Cites Work

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• Summation formulae for finite cotangent sums
• 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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