The trace method for cotangent sums
From MaRDI portal
Publication:2005195
DOI10.1016/j.jcta.2020.105324zbMath1444.11160arXiv2002.06052OpenAlexW3082623713MaRDI QIDQ2005195
Publication date: 7 October 2020
Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2002.06052
combinatorial identitiesinteger valued polynomialsderivative polynomialshigher tangent numberstrigonometric power sum
Combinatorial identities, bijective combinatorics (05A19) Trigonometric and exponential sums (general theory) (11L03) Matrices, determinants in number theory (11C20)
Related Items
An Elementary Derivation of Finite Cotangent Sums ⋮ Human and automated approaches for finite trigonometric sums ⋮ Further developments of basic trigonometric power sums ⋮ Sums of commutators in free probability ⋮ On an approach for evaluating certain trigonometric character sums using the discrete time heat kernel
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Proof of the BMV conjecture
- Basic trigonometric power sums with applications
- Exact evaluations of finite trigonometric sums by sampling theorems
- Higher-order tangent and secant numbers
- Summation formulae for finite cotangent sums
- On the Hurwitz function for rational arguments
- New analytic and computational formalism for the band structure of \(N\)-layer photonic crystals
- Values of the derivatives of the cotangent at rational multiples of \(\pi\)
- Derivative polynomials and closed-form higher derivative formulae
- Combinatorial aspects of continued fractions
- On a trigonometrical sum
- Some Diophantine relations involving circular functions of rational angles
- Derivative polynomials, Euler polynomials, and associated integer sequences
- Partial fractions and trigonometric identities
- Generating functions and generalized Dedekind sums.
- On Chebyshev polynomials and their applications
- Falling coupled oscillators and trigonometric sums
- Reciprocal relations for trigonometric sums
- General order Euler sums with multiple argument
- Explicit evaluations and reciprocity theorems for finite trigonometric sums
- The free tangent law
- Explicit expressions for finite trigonometric sums
- A series transformation formula and related polynomials
- Functions with derivatives given by polynomials in the function itself or a related function
- Higher dimensional Dedekind sums
- Tangent numbers and operators
- ON -VECTORS AND THE DERIVATIVES OF THE TANGENT AND SECANT FUNCTIONS
- Central Factorial Numbers and Values of Bernoulli and Euler Polynomials at Rationals
- Some integer-valued trigonometric sums
- Some polynomials associated with Williams' limit formula for $\zeta (2n)$
- Derivative Polynomials for Tangent and Secant
- A matrix approach to some second-order difference equations with sign-alternating coefficients
- Explicit and asymptotic formulae for Vasyunin-cotangent sums
- Generalized cosecant numbers and trigonometric inverse power sums
- On a finite sum with powers of cosines
- FINITE TRIGONOMETRIC CHARACTER SUMS VIA DISCRETE FOURIER ANALYSIS
- Secant and cosecant sums and Bernoulli-Nörlund polynomials
- Computation of Tangent, Euler, and Bernoulli Numbers
- On ∑<sup>∞</sup><sub>n = 1</sub> (1/n<sup>2k</sup>)
- A Simple Proof of the Formula ∑ ∞ k = 1 = π 2 /6
- Another Elementary Proof of Euler's Formula for ζ(2n)
- Derivative Polynomials for tanh, tan, sech and sec in Explicit Form