x^(1/x) = f^[oo](x) ??

[tommy1729]

As an additional comment I would like to say that if we wanted an iterated power tower a_n^a_(n-1)^...a_0 then this is in some sense the inverse question of my comment to gottfried(*) where we wanted the power tower a_0^a_1^a^2^...

(* http://math.eretrandre.org/tetrationforu...hp?tid=799 )

I know Ramanujan investigated this kind of " inversing " in particular for square root or other root iterations (and continued fraction ofcourse).

http://mathworld.wolfram.com/NestedRadicalConstant.html

And I have been toying with power towers too , such as my " tommyzeta function " here :

http://oeis.org/A102575

A good theory for this seems not yet made ?

regards

tommy1729