05/03/2014, 08:24 PM
Well according to me the value y was between 6.65 and e^2.
This is still true.
Yet I assumed it would be closer to 6.65 due to fast convergeance.
But I guess the " fast " part comes later after more iterations.
I assume sheldon used a computer to do the iterations.
I could not improve the value 6.65 by hand. I havent given it much attention due to lack of time, but if anyone knows how to get 7.28 by hand that would be appreciated.
Im fascinated by how close y is to e^2. I assume this is not coincidence.
Im fascinated by this f(x).
My x_n is now given by f^[-1]( exp^[n] f(x) ).
SO x_n does grow superexponential !
Thank you Sheldon !
2 remaining questions pop up immediately in my head :
1) how fast does f(x) grow ? Can we express f(x) in other functions ?
2) is there a limit form for f^[-1](x) ??
Question 2 reminds me of the idea that finding a limit form of a function that is not given by a sum and that is not analytic is somehow " hard " usually.
Im not quite sure if and why that is true.
With some luck this was already given in the many threads about base change. I did not find the time to investigate this yet.
Thanks for the help !!
And good luck on MSE.
One more thing,
------------------------------------------------------------------------------
Conjecture B : This thread relates to another : http://math.eretrandre.org/tetrationforu...hp?tid=799
More specifically my g(x) and/or H(x) relates to sheldon's f(x) and/or sheldon's f^[-1](x).
Its BTW no coincidence that I gave attention to them again at the same day. In other words I expected this connection for a long time.
------------------------------------------------------------------------------
regards
tommy1729
This is still true.
Yet I assumed it would be closer to 6.65 due to fast convergeance.
But I guess the " fast " part comes later after more iterations.
I assume sheldon used a computer to do the iterations.
I could not improve the value 6.65 by hand. I havent given it much attention due to lack of time, but if anyone knows how to get 7.28 by hand that would be appreciated.
Im fascinated by how close y is to e^2. I assume this is not coincidence.
Im fascinated by this f(x).
My x_n is now given by f^[-1]( exp^[n] f(x) ).
SO x_n does grow superexponential !
Thank you Sheldon !
2 remaining questions pop up immediately in my head :
1) how fast does f(x) grow ? Can we express f(x) in other functions ?
2) is there a limit form for f^[-1](x) ??
Question 2 reminds me of the idea that finding a limit form of a function that is not given by a sum and that is not analytic is somehow " hard " usually.
Im not quite sure if and why that is true.
With some luck this was already given in the many threads about base change. I did not find the time to investigate this yet.
Thanks for the help !!
And good luck on MSE.
One more thing,
------------------------------------------------------------------------------
Conjecture B : This thread relates to another : http://math.eretrandre.org/tetrationforu...hp?tid=799
More specifically my g(x) and/or H(x) relates to sheldon's f(x) and/or sheldon's f^[-1](x).
Its BTW no coincidence that I gave attention to them again at the same day. In other words I expected this connection for a long time.
------------------------------------------------------------------------------
regards
tommy1729
