Euler Product Formula

ζ(s) = Σn⁻ˢ = Π(1−p⁻ˢ)⁻¹ over all primes p. A bridge between analysis and number theory — every integer's unique prime factorization appears in the product.

Parameters

Live Values

ζ(s) exact: —
Sum approx: —
Product approx: —
Relative error: —
ζ(2) = π²/6 ≈ 1.6449
ζ(3) ≈ 1.2021 (Apéry)
ζ(4) = π⁴/90
ζ(s)→1 as s→∞

Riemann: ζ(s) extends
to ℂ\{1} meromorphically