(in progress)
For asymptotic series of iterations of exp(x) see the topic " Fake function theory " !
Below is a link to my profile at the tetration forum.
At the moment I only accept the tetration forum as a good source for tetration although you can find some info and links on wiki , I do however not accept the wiki page.
http://math.eretrandre.org/tetrationforum/member.php?action=profile&uid=47
Thank you for your intrest.
tommy1729