05/07/2014, 12:22 PM
Im searching for an asymptotic to exp[0.5](x).
This is the continuation of the thread http://math.eretrandre.org/tetrationforu...hp?tid=854
where I and sheldon have gone off topic from the OP.
Thus we look for a function with " growth " = 0.5.
Or at least growth between 0 and 1.
Notice f^[n](x) = exp^[m](a^n ln^[m](x))
is not a solution for any m,a.
They all have growth 0.
2 candidates remain :
f1(z) = sum z^n/(n^2)!
f2(z) = ln(z)^e^ln^[3](z)^e^ln^[5]^e^...
We should investigate those perhaps ?
regards
tommy1729
This is the continuation of the thread http://math.eretrandre.org/tetrationforu...hp?tid=854
where I and sheldon have gone off topic from the OP.
Thus we look for a function with " growth " = 0.5.
Or at least growth between 0 and 1.
Notice f^[n](x) = exp^[m](a^n ln^[m](x))
is not a solution for any m,a.
They all have growth 0.
2 candidates remain :
f1(z) = sum z^n/(n^2)!
f2(z) = ln(z)^e^ln^[3](z)^e^ln^[5]^e^...
We should investigate those perhaps ?
regards
tommy1729
