kmath.js Demo — Digamma & Waveshaper
Demo
Docs
Digamma Explorer
Input x
Precision (digamma12)
Evaluate
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
n (integer)
Compute H(n)
H(n) via ψ
H12(n) via ψ₁₂
H(n) = ψ(n+1) + γ
Square Waveshaper (digamma-based)
Parameter b
Samples
Mode
fast (ψ)
precise (ψ₁₂)
Redraw
y = ½( cos(τ b cos a) · (ψ(¾−bc) − ψ(¼−bc))/π − 1 )
drag b to morph the spectrum
Performance & Accuracy
Trials per method
Run benchmark
Speed: steady-state time over fixed-seed dataset. Accuracy: vs reference ψ
ref
=digamma12(x,18) on a mixed sample (edge-cases + random).
API Docs (from JSDoc)
Regenerate
Parses
./kmath.js
comments at runtime.