(28/48/50) Lambert W Function
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04-04-2023, 01:03 AM
(This post was last modified: 04-04-2023 02:26 PM by Albert Chan.)
Post: #27
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RE: (28/48/50) Lambert W Function
(04-03-2023 10:47 PM)Albert Chan Wrote: cos(θ) = ln(|a|/r)/r We can setup solver to get r, then Wk(a) Let c = cos(θ), s = sin(θ) s = (T-θ)/r θ = T-r*s = T - r*√(1-c²) s ≤ 1 → min(r) = T-θ > T-pi lua> g = fn'r,c: c=log(A/r)/r; acos(c) - (T-r*sqrt(1-c*c))' lua> S = require'solver' lua> r = S.secant(g, T-pi, T+pi, nil, true) 29.20162910030975 35.48481440748934 30.766823278237727 30.76703434746101 30.767034374835603 30.767034374835603 lua> c = ln(A/r)/r lua> r * I.new(c, sqrt(1-c*c)) -- = W5(3+4*I) (-1.8170058918466274+30.713334137004896*I) I setup function comparing angles. For |k| ≥ 2, r only have 1 real root. |
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