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lambertw, all branches
01-21-2024, 08:39 PM (This post was last modified: 01-21-2024 09:14 PM by Gil.)
Post: #28
RE: lambertw, all branches
One more question, if I may:

You wrote
"For k=0, I.W code ensured imaginery part is positive (x>0, y≥+0):

W0(-x-y*I) = conj(W-0(conj(-x-y*I))) = conj(W0(-x+y*I))

T = (arg(-x+y*I) + 2*0*pi*I) = arg(-x+y*I)*I = (pi - atan(y/x))*I = (pi/2 .. pi)*I
T/2 = (pi/4 .. pi/2)*I"

a) Suppose that k=0, s=(+1.E-100-i.0000000001).
—> abs(a) < 0.6
Then initial xo = T/2.
Could you give the different step to find the value of T/2?
I found, for xo =T/2, pi/4× PI, but that value leads to endless loops on my program, whereas xo =ln(1+a) gives the expected result.

But here I was lucky.
As I was not sure of the value of T/2,
b) for the other case k=0, a=(-.1,+i×1.E-100),
though abs(a) <0.6,
I tried as the above mentioned case,
xo=ln(1+a),
but then I got endless loops.
What would be the correct step to find here also T/2.

Meanwhile,Takayuki HOSODA's formulae for initial xo gives good, approximate results first digits exact) in both cases a) & b)

Thanks again for your comprehension and possible help.
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Messages In This Thread
lambertw, all branches - Albert Chan - 04-07-2023, 01:24 PM
RE: lambertw, all branches - Albert Chan - 04-07-2023, 02:47 PM
RE: lambertw, all branches - Albert Chan - 04-19-2023, 01:30 AM
RE: lambertw, all branches - pier4r - 04-07-2023, 06:04 PM
RE: lambertw, all branches - Albert Chan - 04-07-2023, 07:54 PM
RE: lambertw, all branches - Albert Chan - 04-08-2023, 03:21 PM
RE: lambertw, all branches - Albert Chan - 04-08-2023, 05:54 PM
RE: lambertw, all branches - Albert Chan - 04-07-2023, 08:40 PM
RE: lambertw, all branches - Albert Chan - 04-09-2023, 03:59 AM
RE: lambertw, all branches - Albert Chan - 04-09-2023, 04:36 PM
RE: lambertw, all branches - Albert Chan - 04-10-2023, 04:44 PM
RE: lambertw, all branches - Albert Chan - 04-10-2023, 06:47 PM
RE: lambertw, all branches - Albert Chan - 04-13-2023, 03:03 PM
RE: lambertw, all branches - floppy - 04-13-2023, 04:14 PM
RE: lambertw, all branches - Albert Chan - 04-23-2023, 02:49 PM
RE: lambertw, all branches - Albert Chan - 04-23-2023, 04:40 PM
RE: lambertw, all branches - Albert Chan - 01-19-2024, 04:14 PM
RE: lambertw, all branches - Albert Chan - 01-20-2024, 04:48 PM
RE: lambertw, all branches - Gil - 01-20-2024, 10:52 PM
RE: lambertw, all branches - Albert Chan - 01-21-2024, 01:14 AM
RE: lambertw, all branches - Albert Chan - 01-21-2024, 01:54 AM
RE: lambertw, all branches - Gil - 01-21-2024, 01:53 PM
RE: lambertw, all branches - Albert Chan - 01-21-2024, 04:19 PM
RE: lambertw, all branches - Gil - 01-21-2024, 04:35 PM
RE: lambertw, all branches - Albert Chan - 01-21-2024, 06:03 PM
RE: lambertw, all branches - Albert Chan - 01-21-2024, 07:01 PM
RE: lambertw, all branches - Gil - 01-21-2024, 07:30 PM
RE: lambertw, all branches - Gil - 01-21-2024 08:39 PM
RE: lambertw, all branches - Albert Chan - 01-21-2024, 10:06 PM
RE: lambertw, all branches - Gil - 01-21-2024, 09:51 PM
RE: lambertw, all branches - Gil - 01-21-2024, 10:56 PM
RE: lambertw, all branches - Albert Chan - 01-22-2024, 01:34 AM
RE: lambertw, all branches - Gil - 01-21-2024, 11:15 PM
RE: lambertw, all branches - Gil - 01-22-2024, 06:09 PM
RE: lambertw, all branches - Albert Chan - 01-22-2024, 07:29 PM
RE: lambertw, all branches - Gil - 01-22-2024, 11:33 PM
RE: lambertw, all branches - Albert Chan - 01-23-2024, 02:32 AM
RE: lambertw, all branches - Gil - 01-23-2024, 02:35 PM
RE: lambertw, all branches - Albert Chan - 01-23-2024, 03:54 PM
RE: lambertw, all branches - Gil - 01-23-2024, 04:57 PM
RE: lambertw, all branches - Albert Chan - 01-23-2024, 06:17 PM
RE: lambertw, all branches - Gil - 01-23-2024, 06:44 PM
RE: lambertw, all branches - Gil - 01-23-2024, 11:00 PM
RE: lambertw, all branches - Gil - 01-24-2024, 03:18 PM
RE: lambertw, all branches - Albert Chan - 01-24-2024, 08:53 PM
RE: lambertw, all branches - Gil - 01-25-2024, 12:37 AM
RE: lambertw, all branches - Gil - 01-25-2024, 01:10 AM
RE: lambertw, all branches - Gil - 01-25-2024, 03:04 AM
RE: lambertw, all branches - Albert Chan - 01-25-2024, 07:02 AM
RE: lambertw, all branches - Gil - 01-25-2024, 10:09 AM
RE: lambertw, all branches - Albert Chan - 01-25-2024, 04:13 PM
RE: lambertw, all branches - Gil - 01-25-2024, 05:14 PM
RE: lambertw, all branches - Albert Chan - 01-25-2024, 05:57 PM
RE: lambertw, all branches - Gil - 01-25-2024, 06:19 PM
RE: lambertw, all branches - Albert Chan - 01-28-2024, 11:18 PM
RE: lambertw, all branches - Albert Chan - 02-01-2024, 02:17 AM
RE: lambertw, all branches - Albert Chan - 02-01-2024, 04:16 PM
RE: lambertw, all branches - Albert Chan - 02-02-2024, 11:49 AM



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