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Lambert W Function (hp-42s)
05-17-2020, 12:12 PM
Post: #6
RE: Lambert W Function (hp-42s)
I don't own a hp-42s, line 21 should be 1E-10 or something like that in the hp-42s. My program can take advantage of the fact that the hp-42s can handle complex numbers. For example let's consider a infinite tower of the imaginary number i, i^i^i^i......
We have i^i^i^i...... = x; i^(i^i^i^i)...... = x; i^x = x or i = x^(1/x) taking ln on both sides of the equation
ln(i) = 1/x ln(x); -ln(i) = -1/x ln(x); -ln(i) = 1/x ln(1/x), calling W to the Lambert W function.
W(-ln(i)) = W(1/x ln(1/x)); W(-ln(i)) = ln(1/x); 1/x = exp(W(-ln(i))) and finally x=exp(-W(-ln(i))).
In the calculator:
0 [ENTER] 1 [COMPLEX] [LN] [+/-] [XEQ] LWF [+/-][■][E↑X]
You get 4.3828293673E-1 i 3.605924718714E-1
so i^i^i^i...... ≈ 0.43828293673+ i 0.3605924718714
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Messages In This Thread
Lambert W Function (hp-42s) - Juan14 - 05-16-2020, 04:07 PM
RE: Lambert W Function (hp-42s) - Werner - 05-17-2020, 07:56 AM
RE: Lambert W Function (hp-42s) - Werner - 05-17-2020, 08:15 AM
RE: Lambert W Function (hp-42s) - Gerald H - 05-17-2020, 09:29 AM
RE: Lambert W Function (hp-42s) - Werner - 05-18-2020, 08:04 AM
RE: Lambert W Function (hp-42s) - Juan14 - 05-17-2020 12:12 PM
RE: Lambert W Function (hp-42s) - Juan14 - 05-18-2020, 10:51 PM
RE: Lambert W Function (hp-42s) - Juan14 - 05-21-2020, 12:09 AM
RE: Lambert W Function (hp-42s) - Werner - 05-22-2020, 11:39 AM
RE: Lambert W Function (hp-42s) - Werner - 05-23-2020, 04:20 AM
RE: Lambert W Function (hp-42s) - Werner - 06-11-2020, 05:17 AM
RE: Lambert W Function (hp-42s) - Werner - 06-11-2020, 09:20 AM
RE: Lambert W Function (hp-42s) - lyuka - 09-28-2020, 04:06 PM
RE: Lambert W Function (hp-42s) - Werner - 09-30-2020, 09:12 AM
RE: Lambert W Function (hp-42s) - Werner - 10-02-2020, 03:02 PM
RE: Lambert W Function (hp-42s) - Werner - 09-30-2020, 07:08 AM
RE: Lambert W Function (hp-42s) - lyuka - 09-29-2020, 09:21 AM
RE: Lambert W Function (hp-42s) - lyuka - 09-29-2020, 11:17 PM
RE: Lambert W Function (hp-42s) - lyuka - 09-30-2020, 11:04 AM
RE: Lambert W Function (hp-42s) - lyuka - 09-30-2020, 07:16 PM
RE: Lambert W Function (hp-42s) - Werner - 10-01-2020, 09:37 AM
RE: Lambert W Function (hp-42s) - Werner - 10-01-2020, 01:39 PM
RE: Lambert W Function (hp-42s) - lyuka - 10-01-2020, 06:25 PM
RE: Lambert W Function (hp-42s) - lyuka - 10-02-2020, 05:44 AM
RE: Lambert W Function (hp-42s) - lyuka - 10-03-2020, 07:56 PM
RE: Lambert W Function (hp-42s) - Werner - 10-05-2020, 08:03 AM
RE: Lambert W Function (hp-42s) - lyuka - 10-05-2020, 06:09 PM
RE: Lambert W Function (hp-42s) - Werner - 10-06-2020, 06:16 AM
RE: Lambert W Function (hp-42s) - lyuka - 11-09-2020, 08:30 AM



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