Apa itu Konstanta Omega?

Fixed-point iteration: e^(−x) converging to Ω

Starting from x=0.5, repeatedly applying e^(−x) converges to Ω ≈ 0.5671. The fixed point satisfies Ω = e^(−Ω), equivalently Ω·e^Ω = 1.

Iterasi	x	e^(−x)	\|x − Ω\|
1	0,5	0,60653	0,067
2	0,60653	0,54545	0,022
3	0,54545	0,57970	0,008
4	0,57970	0,56007	0,003
5	0,56007	0,57121	0,001
…	…	…	→ 0
∞	Ω	Ω	0

Lambert W function: where Ω appears

W(xe^x) = x  →  Ω = W(1)  ≈  0.56714

Ω solves xe^x = 1. It appears in delay differential equations, Lagrange points, iterated exponentials (e^e^e…), and in the time complexity of certain sorting algorithms.

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