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.
Digunakan dalam
Matematika
✓
Fisika
✓
Teknik
✓
Biologi
–
Ilmu Komputer
✓
Statistika
–
Keuangan
–
Seni
–
Arsitektur
–
Musik
–
Kriptografi
–
Astronomi
–
Kimia
–
Filsafat
–
Geografi
–
Ekologi
–
Ingin menguji pengetahuan Anda?
Pertanyaan
Apa identitas referensi-diri yang dipenuhi Ω?
ketuk · spasi
1 / 10
Siap bermain?
Pi
Memorize pi, e, and 40+ mathematical constants using the numpad path method
Main sekarang - gratisTanpa akun. Bisa di perangkat apa saja.
Topic roundups
