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(28/48/50) Lambert W Function
04-04-2023, 01:03 AM (This post was last modified: 04-04-2023 02:26 PM by Albert Chan.)
Post: #27
RE: (28/48/50) Lambert W Function
(04-03-2023 10:47 PM)Albert Chan Wrote:  cos(θ) = ln(|a|/r)/r
sin(θ) = (T-θ)/r

We assume k positive --> both r and x imag part positive too.

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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Messages In This Thread
(28/48/50) Lambert W Function - John Keith - 03-20-2023, 08:43 PM
RE: (28/48/50) Lambert W Function - Albert Chan - 04-04-2023 01:03 AM
RE: (28/48/50) Lambert W Function - Gil - 01-29-2024, 11:04 AM
RE: (28/48/50) Lambert W Function - Gil - 01-29-2024, 02:47 PM
RE: (28/48/50) Lambert W Function - Gil - 01-29-2024, 06:46 PM
RE: (28/48/50) Lambert W Function - Gil - 01-29-2024, 09:50 PM
RE: (28/48/50) Lambert W Function - Gil - 01-30-2024, 12:33 AM
RE: (28/48/50) Lambert W Function - Gil - 01-30-2024, 12:04 PM
RE: (28/48/50) Lambert W Function - Gil - 01-30-2024, 02:52 PM
RE: (28/48/50) Lambert W Function - Gil - 01-31-2024, 07:10 PM



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