kmath.js Demo — Digamma & Waveshaper

Digamma Explorer

Poles at x ∈ {0, −1, −2, ...}
Reflection: ψ(1−x) − ψ(x) = π cot(πx)
ψ(x) fast
ψ(x) digamma12
|Δ|
Known values: ψ(1) = −γ, ψ(1/2) = −γ − 2 ln 2.

Harmonic Numbers

H(n) via ψ
H12(n) via ψ₁₂
H(n) = ψ(n+1) + γ

Square Waveshaper (digamma-based)

y = ½( cos(τ b cos a) · (ψ(¾−bc) − ψ(¼−bc))/π − 1 )
drag b to morph the spectrum

Performance & Accuracy

Speed: steady-state time over fixed-seed dataset. Accuracy: vs reference ψref=digamma12(x,18) on a mixed sample (edge-cases + random).

API Docs (from JSDoc)

Parses ./kmath.js comments at runtime.