The ~9% overshoot that never disappears, no matter how many terms
Series
Auto-increment
Harmonics (live)
Gibbs overshoot = 0.00%
Max error = 0.00
L² error = 0.00
Theory
Gibbs limit: 8.9% overshoot regardless of N → ∞. Converges in L² but NOT uniformly near discontinuity.
Partial sum order: 5
Lanczos σ-factor: smooths Gibbs (toggle)
Physics / Math: The Fourier series of a discontinuous function converges pointwise except at the jump, where it converges to the midpoint. Near the jump, the partial sums overshoot by ~9% of the jump height — the Gibbs phenomenon (Wilbraham 1848, Gibbs 1899). Specifically, the overshoot → (2/π)∫₀^π sin(x)/x dx − 1 ≈ 0.0895... for a unit-height jump. This is NOT a numerical artifact — it occurs for the exact partial sum at every N. The Lanczos σ-factor (multiply coefficient cₙ by sinc(nπ/N)) damps the overshoot at the cost of smearing the edge.