Apa itu Aproksimasi Stirling?

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Stirling approximation: relative error rapidly → 0

The relative error |n! − Stirling(n)| / n! falls below 1% at n = 8 and below 0.1% at n = 80. For large n, Stirling is essentially exact.

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Stirling's formula: logarithmic form

ln(n!) ≈ n·ln(n) − n + ½·ln(2πn)

Equivalent: n! ≈ √(2πn) · (n/e)ⁿ

Relative error → 0 as n → ∞. Exact for all practical purposes when n ≥ 20.

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log(n!) grows exactly as Stirling predicts

On a log scale, n! and Stirlings approximation are visually identical. Relative error approaches 0 as n grows.

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