03/30/2021, 03:24 PM
(This post was last modified: 03/30/2021, 03:56 PM by nuninho1980.)
(03/28/2021, 06:26 AM)Daniel Wrote: Howdy,
Check out a question on extending tetration. I'm inviting folks to critic my answers or to provide your own.
Daniel
I use Maple 2020.
base^^x = f(x) = lim n -> infinity (log_base[n](1 - ln(W(-ln(base))/(-ln(base)))^x)*W(-ln(base))/(-ln(base)) + ln(W(-ln(base))/(-ln(base)))*exp_base[n](1)))
--> Is this formula correct? But...
On Maple -- n = 10 times:
- input
---------------------------------------------------------------------------------------------------------------------------
Digits:=20:
base:=1.35: x:=2.:
log[base](log[base](log[base](log[base](log[base](log[base](log[base](log[base](log[base](log[base]((1 - ln(LambertW(-ln(base))/(-ln(base)))^x)*LambertW(-ln(base))/(-ln(base)) + ln(LambertW(-ln(base))/(-ln(base)))*base^(base^(base^(base^(base^(base^(base^(base^(base^(base^base)))))))))))))))))));
---------------------------------------------------------------------------------------------------------------------------
- output
--------------------------------
5.8512341052940943912
--------------------------------
--> This output is incorrect...
1.35^^2 = 1.4995142162286330979 --> this is correct.