A periodic function with period 2π can be expanded as Σ(a_n cos nx + b_n sin nx), with coefficients given by orthogonality integrals. Converges to f at points of continuity.
Fourier series
Related concepts
- Series convergence
- Orthogonality
- Orthogonality
- Heat equation
- Lp space
- Poisson integral normalisation: ∫₀^{2π} P_{1/2}(θ) dθ/(2π) ≡ 1
- Dirichlet theorem on APs (1837)
- Fejer kernel (Cesaro summation 1900)
- FFT & digital signal processing
- Betatron oscillation Floquet spectrum (accelerator-physics)
- Rossby wave dispersion from β-plane geostrophy (geophysics)
- Kaluza–Klein reduction
- Winfree phase response curve: Δφ(φ)=A·sin(φ); sinusoidal entrainment Fourier-mode