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