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.